inputs stringlengths 24 1.5k | choices_list listlengths 2 63 | labels int64 0 57 | metadata stringlengths 120 157 |
|---|---|---|---|
For the lines of any plane , | p , meeting Q in a conic C , are transformed into the congruence of secants of the curve C ' into which C is [TARGET] transformed [/TARGET] in the point involution on Q . | [
"change or alter in form, appearance, or nature; \"This experience transformed her completely\"; \"She transformed the clay into a beautiful sculpture\"",
"change from one form or medium into another; \"Braque translated collage into oil\"",
"subject to a mathematical transformation",
"change in outward struc... | 2 | {"id": "br-j21:22:33", "sense_key": "transform%2:30:02::", "split_group_id": "br-j21", "token_index": 33, "wordnet_version": "1.6"} |
In particular , tangents to C are [TARGET] transformed [/TARGET] into tangents to C ' . | [
"change or alter in form, appearance, or nature; \"This experience transformed her completely\"; \"She transformed the clay into a beautiful sculpture\"",
"change from one form or medium into another; \"Braque translated collage into oil\"",
"subject to a mathematical transformation",
"change in outward struc... | 2 | {"id": "br-j21:23:6", "sense_key": "transform%2:30:02::", "split_group_id": "br-j21", "token_index": 6, "wordnet_version": "1.6"} |
Moreover , if * * f and * * f [TARGET] are [/TARGET] two planes intersecting in a line l , tangent to Q at a point P , the two free intersections of the image curves * * f and * * f must coincide at P ' , the image of P , and at this point * * f and * * f must have a common tangent l ' . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 8 | {"id": "br-j21:24:10", "sense_key": "be%2:42:06::", "split_group_id": "br-j21", "token_index": 10, "wordnet_version": "1.6"} |
Moreover , if * * f and * * f are two planes intersecting in a line l , tangent to Q at a point P , the two free intersections of the image curves * * f and * * f must [TARGET] coincide [/TARGET] at P ' , the image of P , and at this point * * f and * * f must have a common tangent l ' . | [
"happen simultaneously; \"The two events coincided\"",
"go_with, fall together",
"be the same; \"our views on this matter coincided\""
] | 1 | {"id": "br-j21:24:43", "sense_key": "coincide%2:42:00::", "split_group_id": "br-j21", "token_index": 43, "wordnet_version": "1.6"} |
Moreover , if * * f and * * f are two planes intersecting in a line l , tangent to Q at a point P , the two free intersections of the image curves * * f and * * f must coincide at P ' , the image of P , and at this point * * f and * * f must [TARGET] have [/TARGET] a common tangent l ' . | [
"give birth (to a newborn); \"My wife had twins yesterday!\"",
"suffer from; be ill with; \"She has arthritis\"",
"of injuries and illnesses: \"She suffered a fracture in the accident\"; \"He had an insulin shock after eating three candy bars\"; \"She got a bruise on her leg\"; \"He got his arm broken in the sc... | 17 | {"id": "br-j21:24:65", "sense_key": "have%2:42:00::", "split_group_id": "br-j21", "token_index": 65, "wordnet_version": "1.6"} |
Hence , [TARGET] thought of [/TARGET] as a line in a particular plane | p , any tangent to Q has a unique image and moreover this image is the same for all planes through l . | [
"keep in mind for attention or consideration; \"Remember the Alamo\"; \"Remember to call your mother every day!\"; \"Think of the starving children in India!\"",
"look on as or consider: \"she looked on this affair as a joke\"; \"He thinks of himself as a brilliant musician\"",
"\"I'm thinking of good food when... | 1 | {"id": "br-j21:25:2", "sense_key": "think_of%2:31:01::", "split_group_id": "br-j21", "token_index": 2, "wordnet_version": "1.6"} |
Hence , thought of as a line in a particular plane | p , any tangent to Q [TARGET] has [/TARGET] a unique image and moreover this image is the same for all planes through l . | [
"give birth (to a newborn); \"My wife had twins yesterday!\"",
"suffer from; be ill with; \"She has arthritis\"",
"of injuries and illnesses: \"She suffered a fracture in the accident\"; \"He had an insulin shock after eating three candy bars\"; \"She got a bruise on her leg\"; \"He got his arm broken in the sc... | 17 | {"id": "br-j21:25:17", "sense_key": "have%2:42:00::", "split_group_id": "br-j21", "token_index": 17, "wordnet_version": "1.6"} |
Hence , thought of as a line in a particular plane | p , any tangent to Q has a unique image and moreover this image [TARGET] is [/TARGET] the same for all planes through l . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 5 | {"id": "br-j21:25:25", "sense_key": "be%2:42:03::", "split_group_id": "br-j21", "token_index": 25, "wordnet_version": "1.6"} |
Each generator , | l , of * * f [TARGET] is [/TARGET] also exceptional , for each is transformed into the entire congruence of secants of the curve into which that generator is transformed by the point involution on Q . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 5 | {"id": "br-j21:26:10", "sense_key": "be%2:42:03::", "split_group_id": "br-j21", "token_index": 10, "wordnet_version": "1.6"} |
Each generator , | l , of * * f is also exceptional , for each is [TARGET] transformed [/TARGET] into the entire congruence of secants of the curve into which that generator is transformed by the point involution on Q . | [
"change or alter in form, appearance, or nature; \"This experience transformed her completely\"; \"She transformed the clay into a beautiful sculpture\"",
"change from one form or medium into another; \"Braque translated collage into oil\"",
"subject to a mathematical transformation",
"change in outward struc... | 2 | {"id": "br-j21:26:17", "sense_key": "transform%2:30:02::", "split_group_id": "br-j21", "token_index": 17, "wordnet_version": "1.6"} |
Each generator , | l , of * * f is also exceptional , for each is transformed into the entire congruence of secants of the curve into which that generator is [TARGET] transformed [/TARGET] by the point involution on Q . | [
"change or alter in form, appearance, or nature; \"This experience transformed her completely\"; \"She transformed the clay into a beautiful sculpture\"",
"change from one form or medium into another; \"Braque translated collage into oil\"",
"subject to a mathematical transformation",
"change in outward struc... | 2 | {"id": "br-j21:26:32", "sense_key": "transform%2:30:02::", "split_group_id": "br-j21", "token_index": 32, "wordnet_version": "1.6"} |
This curve [TARGET] is [/TARGET] of symbol * * f since it meets | l , and hence every line of * * f in the * * f invariant points on | l and since it obviously meets every line of * * f in a single point . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 5 | {"id": "br-j21:27:2", "sense_key": "be%2:42:03::", "split_group_id": "br-j21", "token_index": 2, "wordnet_version": "1.6"} |
This curve is of symbol * * f since it [TARGET] meets [/TARGET] | l , and hence every line of * * f in the * * f invariant points on | l and since it obviously meets every line of * * f in a single point . | [
"contend against an opponent in a sport, game, or battle; \"Princeton plays Yale this weekend\"; \"Charlie likes to play Mary\"",
"fill or meet a want or need",
"be in contact with",
"get or come together; \"the two lines meet here\"",
"meet; \"I'll probably see you at the meeting\"; \"How nice to see you a... | 13 | {"id": "br-j21:27:10", "sense_key": "meet%2:42:02::", "split_group_id": "br-j21", "token_index": 10, "wordnet_version": "1.6"} |
This curve is of symbol * * f since it meets | l , and hence every line of * * f in the * * f invariant points on | l and since it obviously [TARGET] meets [/TARGET] every line of * * f in a single point . | [
"contend against an opponent in a sport, game, or battle; \"Princeton plays Yale this weekend\"; \"Charlie likes to play Mary\"",
"fill or meet a want or need",
"be in contact with",
"get or come together; \"the two lines meet here\"",
"meet; \"I'll probably see you at the meeting\"; \"How nice to see you a... | 13 | {"id": "br-j21:27:36", "sense_key": "meet%2:42:02::", "split_group_id": "br-j21", "token_index": 36, "wordnet_version": "1.6"} |
The congruence of its secants [TARGET] is [/TARGET] therefore of order * * f and class * * f . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 5 | {"id": "br-j21:28:5", "sense_key": "be%2:42:03::", "split_group_id": "br-j21", "token_index": 5, "wordnet_version": "1.6"} |
A final class of exceptional lines [TARGET] is [/TARGET] identifiable from the following considerations : Since no two generators of * * f can intersect , it follows that their image curves can have no free intersections . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 5 | {"id": "br-j21:29:6", "sense_key": "be%2:42:03::", "split_group_id": "br-j21", "token_index": 6, "wordnet_version": "1.6"} |
A final class of exceptional lines is identifiable from the following considerations : Since no two generators of * * f can intersect , it [TARGET] follows [/TARGET] that their image curves can have no free intersections . | [
"behave in accordance or in agreement with; \"Follow a pattern\"; \"Follow my example\"",
"keep informed; \"He kept up on his country's foreign policies\"",
"keep to: \"Stick to your principles\"; \"stick to the diet\"",
"follow, discover, or ascertain the course of development of something; \"We must follow ... | 23 | {"id": "br-j21:29:25", "sense_key": "follow%2:42:05::", "split_group_id": "br-j21", "token_index": 25, "wordnet_version": "1.6"} |
A final class of exceptional lines is identifiable from the following considerations : Since no two generators of * * f can intersect , it follows that their image curves can [TARGET] have [/TARGET] no free intersections . | [
"give birth (to a newborn); \"My wife had twins yesterday!\"",
"suffer from; be ill with; \"She has arthritis\"",
"of injuries and illnesses: \"She suffered a fracture in the accident\"; \"He had an insulin shock after eating three candy bars\"; \"She got a bruise on her leg\"; \"He got his arm broken in the sc... | 17 | {"id": "br-j21:29:31", "sense_key": "have%2:42:00::", "split_group_id": "br-j21", "token_index": 31, "wordnet_version": "1.6"} |
In other words , these curves [TARGET] have [/TARGET] only fixed intersections common to them all . | [
"give birth (to a newborn); \"My wife had twins yesterday!\"",
"suffer from; be ill with; \"She has arthritis\"",
"of injuries and illnesses: \"She suffered a fracture in the accident\"; \"He had an insulin shock after eating three candy bars\"; \"She got a bruise on her leg\"; \"He got his arm broken in the sc... | 17 | {"id": "br-j21:30:4", "sense_key": "have%2:42:00::", "split_group_id": "br-j21", "token_index": 4, "wordnet_version": "1.6"} |
Now the only way in which all curves of the image family of * * f can [TARGET] pass [/TARGET] through a fixed point is to have a generator of * * f which is not a secant but a tangent of \ g , for then any point on such a generator will be transformed into the point of tangency . | [
"eliminate from the body; \"Pass a kidney stone\"",
"come to pass; occur: \"What is happening?\"; \"The meeting took place off without an incidence\"; \"Nothing occurred that seemed important\"",
"disappear gradually; as of emotions, for example; \"The pain eventually passed off\"",
"grant authorization or cl... | 24 | {"id": "br-j21:31:16", "sense_key": "pass%2:42:08::", "split_group_id": "br-j21", "token_index": 16, "wordnet_version": "1.6"} |
Now the only way in which all curves of the image family of * * f can pass through a fixed point [TARGET] is [/TARGET] to have a generator of * * f which is not a secant but a tangent of \ g , for then any point on such a generator will be transformed into the point of tangency . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 8 | {"id": "br-j21:31:21", "sense_key": "be%2:42:06::", "split_group_id": "br-j21", "token_index": 21, "wordnet_version": "1.6"} |
Now the only way in which all curves of the image family of * * f can pass through a fixed point is to [TARGET] have [/TARGET] a generator of * * f which is not a secant but a tangent of \ g , for then any point on such a generator will be transformed into the point of tangency . | [
"give birth (to a newborn); \"My wife had twins yesterday!\"",
"suffer from; be ill with; \"She has arthritis\"",
"of injuries and illnesses: \"She suffered a fracture in the accident\"; \"He had an insulin shock after eating three candy bars\"; \"She got a bruise on her leg\"; \"He got his arm broken in the sc... | 10 | {"id": "br-j21:31:23", "sense_key": "have%2:40:00::", "split_group_id": "br-j21", "token_index": 23, "wordnet_version": "1.6"} |
Now the only way in which all curves of the image family of * * f can pass through a fixed point is to have a generator of * * f which [TARGET] is [/TARGET] not a secant but a tangent of \ g , for then any point on such a generator will be transformed into the point of tangency . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 8 | {"id": "br-j21:31:31", "sense_key": "be%2:42:06::", "split_group_id": "br-j21", "token_index": 31, "wordnet_version": "1.6"} |
Now the only way in which all curves of the image family of * * f can pass through a fixed point is to have a generator of * * f which is not a secant but a tangent of \ g , for then any point on such a generator will be [TARGET] transformed [/TARGET] into the point of tangency . | [
"change or alter in form, appearance, or nature; \"This experience transformed her completely\"; \"She transformed the clay into a beautiful sculpture\"",
"change from one form or medium into another; \"Braque translated collage into oil\"",
"subject to a mathematical transformation",
"change in outward struc... | 2 | {"id": "br-j21:31:52", "sense_key": "transform%2:30:02::", "split_group_id": "br-j21", "token_index": 52, "wordnet_version": "1.6"} |
Since two curves of symbol * * f on Q intersect in * * f points , it [TARGET] follows [/TARGET] that there are * * f lines of * * f which are tangent to \ g . | [
"behave in accordance or in agreement with; \"Follow a pattern\"; \"Follow my example\"",
"keep informed; \"He kept up on his country's foreign policies\"",
"keep to: \"Stick to your principles\"; \"stick to the diet\"",
"follow, discover, or ascertain the course of development of something; \"We must follow ... | 23 | {"id": "br-j21:32:18", "sense_key": "follow%2:42:05::", "split_group_id": "br-j21", "token_index": 18, "wordnet_version": "1.6"} |
Since two curves of symbol * * f on Q intersect in * * f points , it follows that there are * * f lines of * * f which [TARGET] are [/TARGET] tangent to \ g . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 5 | {"id": "br-j21:32:31", "sense_key": "be%2:42:03::", "split_group_id": "br-j21", "token_index": 31, "wordnet_version": "1.6"} |
Clearly , any line , l , of any bundle [TARGET] having [/TARGET] one of these points of tangency , T , as vertex will be transformed into the entire pencil having the image of the second intersection of l and Q as vertex and lying in the plane determined by the image point and the generator of * * f which is tangent to... | [
"give birth (to a newborn); \"My wife had twins yesterday!\"",
"suffer from; be ill with; \"She has arthritis\"",
"of injuries and illnesses: \"She suffered a fracture in the accident\"; \"He had an insulin shock after eating three candy bars\"; \"She got a bruise on her leg\"; \"He got his arm broken in the sc... | 10 | {"id": "br-j21:33:10", "sense_key": "have%2:40:00::", "split_group_id": "br-j21", "token_index": 10, "wordnet_version": "1.6"} |
Clearly , any line , l , of any bundle having one of these points of tangency , T , as vertex will be [TARGET] transformed [/TARGET] into the entire pencil having the image of the second intersection of l and Q as vertex and lying in the plane determined by the image point and the generator of * * f which is tangent to... | [
"change or alter in form, appearance, or nature; \"This experience transformed her completely\"; \"She transformed the clay into a beautiful sculpture\"",
"change from one form or medium into another; \"Braque translated collage into oil\"",
"subject to a mathematical transformation",
"change in outward struc... | 2 | {"id": "br-j21:33:24", "sense_key": "transform%2:30:02::", "split_group_id": "br-j21", "token_index": 24, "wordnet_version": "1.6"} |
Clearly , any line , l , of any bundle having one of these points of tangency , T , as vertex will be transformed into the entire pencil [TARGET] having [/TARGET] the image of the second intersection of l and Q as vertex and lying in the plane determined by the image point and the generator of * * f which is tangent to... | [
"give birth (to a newborn); \"My wife had twins yesterday!\"",
"suffer from; be ill with; \"She has arthritis\"",
"of injuries and illnesses: \"She suffered a fracture in the accident\"; \"He had an insulin shock after eating three candy bars\"; \"She got a bruise on her leg\"; \"He got his arm broken in the sc... | 10 | {"id": "br-j21:33:29", "sense_key": "have%2:40:00::", "split_group_id": "br-j21", "token_index": 29, "wordnet_version": "1.6"} |
Clearly , any line , l , of any bundle having one of these points of tangency , T , as vertex will be transformed into the entire pencil having the image of the second intersection of l and Q as vertex and [TARGET] lying [/TARGET] in the plane determined by the image point and the generator of * * f which is tangent to... | [
"tell an untruth; pretend with intent to deceive; \"Don't lie to your parents\"; \"She lied when she told me she was only 29\"",
"be lying, be prostrate; be in a horizontal position; \"The sick man lay in bed all day\"l \"the books are lying on the shelf\"",
"assume a resting position, as on a flat surface",
... | 4 | {"id": "br-j21:33:43", "sense_key": "lie%2:42:00::", "split_group_id": "br-j21", "token_index": 43, "wordnet_version": "1.6"} |
Clearly , any line , l , of any bundle having one of these points of tangency , T , as vertex will be transformed into the entire pencil having the image of the second intersection of l and Q as vertex and lying in the plane [TARGET] determined [/TARGET] by the image point and the generator of * * f which is tangent to... | [
"reach, make, or come to a decision about something; \"We finally decided after lengthy deliberations\"",
"fix conclusively or authoritatively; \"set the rules\"",
"shape or influence; give direction to; \"experience often determines ability\"",
"fix in scope; fix the boundaries of; the tree determines the bo... | 3 | {"id": "br-j21:33:47", "sense_key": "determine%2:31:03::", "split_group_id": "br-j21", "token_index": 47, "wordnet_version": "1.6"} |
Clearly , any line , l , of any bundle having one of these points of tangency , T , as vertex will be transformed into the entire pencil having the image of the second intersection of l and Q as vertex and lying in the plane determined by the image point and the generator of * * f which [TARGET] is [/TARGET] tangent to... | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 5 | {"id": "br-j21:33:60", "sense_key": "be%2:42:03::", "split_group_id": "br-j21", "token_index": 60, "wordnet_version": "1.6"} |
A line through two of these points , * * f and * * f , will be [TARGET] transformed [/TARGET] into the entire bilinear congruence having the tangents to \ g at * * f and * * f as directrices . | [
"change or alter in form, appearance, or nature; \"This experience transformed her completely\"; \"She transformed the clay into a beautiful sculpture\"",
"change from one form or medium into another; \"Braque translated collage into oil\"",
"subject to a mathematical transformation",
"change in outward struc... | 2 | {"id": "br-j21:34:18", "sense_key": "transform%2:30:02::", "split_group_id": "br-j21", "token_index": 18, "wordnet_version": "1.6"} |
A line through two of these points , * * f and * * f , will be transformed into the entire bilinear congruence [TARGET] having [/TARGET] the tangents to \ g at * * f and * * f as directrices . | [
"give birth (to a newborn); \"My wife had twins yesterday!\"",
"suffer from; be ill with; \"She has arthritis\"",
"of injuries and illnesses: \"She suffered a fracture in the accident\"; \"He had an insulin shock after eating three candy bars\"; \"She got a bruise on her leg\"; \"He got his arm broken in the sc... | 10 | {"id": "br-j21:34:24", "sense_key": "have%2:40:00::", "split_group_id": "br-j21", "token_index": 24, "wordnet_version": "1.6"} |
A conic , C , [TARGET] being [/TARGET] a ( 1 , 1 ) curve on Q , meets the image of any line of * * f , which we have already found to be a * * f curve on Q , in * * f points . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 8 | {"id": "br-j21:35:5", "sense_key": "be%2:42:06::", "split_group_id": "br-j21", "token_index": 5, "wordnet_version": "1.6"} |
A conic , C , being a ( 1 , 1 ) curve on Q , [TARGET] meets [/TARGET] the image of any line of * * f , which we have already found to be a * * f curve on Q , in * * f points . | [
"contend against an opponent in a sport, game, or battle; \"Princeton plays Yale this weekend\"; \"Charlie likes to play Mary\"",
"fill or meet a want or need",
"be in contact with",
"get or come together; \"the two lines meet here\"",
"meet; \"I'll probably see you at the meeting\"; \"How nice to see you a... | 13 | {"id": "br-j21:35:16", "sense_key": "meet%2:42:02::", "split_group_id": "br-j21", "token_index": 16, "wordnet_version": "1.6"} |
A conic , C , being a ( 1 , 1 ) curve on Q , meets the image of any line of * * f , which we have already [TARGET] found [/TARGET] to be a * * f curve on Q , in * * f points . | [
"receive a specified treatment (abstract); \"These aspects of civilization do not find expression or receive an interpretation\"; \"His movie received a good review\"; \"I got nothing but trouble for my good intentions\"",
"make a discovery; \"She found that he had lied to her\"; \"The story is false, so far as I... | 4 | {"id": "br-j21:35:31", "sense_key": "find%2:32:00::", "split_group_id": "br-j21", "token_index": 31, "wordnet_version": "1.6"} |
A conic , C , being a ( 1 , 1 ) curve on Q , meets the image of any line of * * f , which we have already found to [TARGET] be [/TARGET] a * * f curve on Q , in * * f points . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 8 | {"id": "br-j21:35:33", "sense_key": "be%2:42:06::", "split_group_id": "br-j21", "token_index": 33, "wordnet_version": "1.6"} |
Hence its image , C ' , [TARGET] meets [/TARGET] any line of * * f in * * f points . | [
"contend against an opponent in a sport, game, or battle; \"Princeton plays Yale this weekend\"; \"Charlie likes to play Mary\"",
"fill or meet a want or need",
"be in contact with",
"get or come together; \"the two lines meet here\"",
"meet; \"I'll probably see you at the meeting\"; \"How nice to see you a... | 13 | {"id": "br-j21:36:7", "sense_key": "meet%2:42:02::", "split_group_id": "br-j21", "token_index": 7, "wordnet_version": "1.6"} |
Moreover , C ' obviously [TARGET] meets [/TARGET] any line * * f in a single point . | [
"contend against an opponent in a sport, game, or battle; \"Princeton plays Yale this weekend\"; \"Charlie likes to play Mary\"",
"fill or meet a want or need",
"be in contact with",
"get or come together; \"the two lines meet here\"",
"meet; \"I'll probably see you at the meeting\"; \"How nice to see you a... | 13 | {"id": "br-j21:37:5", "sense_key": "meet%2:42:02::", "split_group_id": "br-j21", "token_index": 5, "wordnet_version": "1.6"} |
Hence C ' [TARGET] is [/TARGET] a * * f curve on Q . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 8 | {"id": "br-j21:38:3", "sense_key": "be%2:42:06::", "split_group_id": "br-j21", "token_index": 3, "wordnet_version": "1.6"} |
Therefore , the congruence of its secants , that is the image of a general plane field of lines , [TARGET] is [/TARGET] of order * * f and class * * f . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 5 | {"id": "br-j21:39:19", "sense_key": "be%2:42:03::", "split_group_id": "br-j21", "token_index": 19, "wordnet_version": "1.6"} |
Finally , the image of a general bundle of lines [TARGET] is [/TARGET] a congruence whose order is the order of the congruence of invariant lines , namely * * f and whose class is the order of the image congruence of a general plane field of lines , namely * * f . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 8 | {"id": "br-j21:40:10", "sense_key": "be%2:42:06::", "split_group_id": "br-j21", "token_index": 10, "wordnet_version": "1.6"} |
Finally , the image of a general bundle of lines is a congruence whose order [TARGET] is [/TARGET] the order of the congruence of invariant lines , namely * * f and whose class is the order of the image congruence of a general plane field of lines , namely * * f . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 8 | {"id": "br-j21:40:15", "sense_key": "be%2:42:06::", "split_group_id": "br-j21", "token_index": 15, "wordnet_version": "1.6"} |
Finally , the image of a general bundle of lines is a congruence whose order is the order of the congruence of invariant lines , namely * * f and whose class [TARGET] is [/TARGET] the order of the image congruence of a general plane field of lines , namely * * f . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 8 | {"id": "br-j21:40:32", "sense_key": "be%2:42:06::", "split_group_id": "br-j21", "token_index": 32, "wordnet_version": "1.6"} |
The preceding observations [TARGET] make [/TARGET] it clear that there exist line involutions of all orders greater than 1 with no complex of invariant lines and with a complex of singular lines consisting exclusively of the lines which meet a twisted curve \ g . | [
"have a bowel movement; \"The dog had made in the flower beds\"",
"eliminate urine; \"Again, the cat had made on the expensive rug\"",
"behave in a certain way; \"make merry\"",
"act in a certain way so as to acquire; \"make friends\"; \"make enemies\"",
"give certain properties to something; \"get someone ... | 4 | {"id": "br-j21:41:3", "sense_key": "make%2:30:00::", "split_group_id": "br-j21", "token_index": 3, "wordnet_version": "1.6"} |
The preceding observations make it clear that there [TARGET] exist [/TARGET] line involutions of all orders greater than 1 with no complex of invariant lines and with a complex of singular lines consisting exclusively of the lines which meet a twisted curve \ g . | [
"have an existence, be extant; \"Is there a God?\"",
"stay alive; survive; \"he could barely exist on such a low wage\""
] | 0 | {"id": "br-j21:41:8", "sense_key": "exist%2:42:00::", "split_group_id": "br-j21", "token_index": 8, "wordnet_version": "1.6"} |
The preceding observations make it clear that there exist line involutions of all orders greater than 1 with no complex of invariant lines and with a complex of singular lines [TARGET] consisting [/TARGET] exclusively of the lines which meet a twisted curve \ g . | [
"be composed of; \"What does this dish consist of?\"",
"be composed of; \"The land he conquered comprised several provinces\""
] | 0 | {"id": "br-j21:41:30", "sense_key": "consist_of%2:42:00::", "split_group_id": "br-j21", "token_index": 30, "wordnet_version": "1.6"} |
The preceding observations make it clear that there exist line involutions of all orders greater than 1 with no complex of invariant lines and with a complex of singular lines consisting exclusively of the lines which [TARGET] meet [/TARGET] a twisted curve \ g . | [
"contend against an opponent in a sport, game, or battle; \"Princeton plays Yale this weekend\"; \"Charlie likes to play Mary\"",
"fill or meet a want or need",
"be in contact with",
"get or come together; \"the two lines meet here\"",
"meet; \"I'll probably see you at the meeting\"; \"How nice to see you a... | 13 | {"id": "br-j21:41:36", "sense_key": "meet%2:42:02::", "split_group_id": "br-j21", "token_index": 36, "wordnet_version": "1.6"} |
We now shall [TARGET] show [/TARGET] that any involution with these characteristics is necessarily of the type we have just described . | [
"establish the validity of something; \"This behavior shows his true nature\"",
"provide evidence for; \"The blood test showed that he was the father\"; \"Her behavior testified to her incompetence\"",
"indicate a place, direction, person, or thing; either spatially or figuratively; \"I showed the customer the ... | 1 | {"id": "br-j21:42:3", "sense_key": "show%2:32:00::", "split_group_id": "br-j21", "token_index": 3, "wordnet_version": "1.6"} |
We now shall show that any involution with these characteristics [TARGET] is [/TARGET] necessarily of the type we have just described . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 8 | {"id": "br-j21:42:10", "sense_key": "be%2:42:06::", "split_group_id": "br-j21", "token_index": 10, "wordnet_version": "1.6"} |
We now shall show that any involution with these characteristics is necessarily of the type we have just [TARGET] described [/TARGET] . | [
"as in in botany or biology, for example",
"give a description of; \"He drew an elaborate plan of attack\"",
"to give an account or representation of in words: \"Discreet Italian police described it in a manner typically continental.\"",
"make a mark or lines on a surface; \"draw a line\"; \"draw the outlines... | 2 | {"id": "br-j21:42:18", "sense_key": "describe%2:32:01::", "split_group_id": "br-j21", "token_index": 18, "wordnet_version": "1.6"} |
To [TARGET] do [/TARGET] this we must first show that every line which meets \ g in a point P meets its image at P . | [
"of hair",
"behave in a certain manner; show a certain behavior; conduct or comport oneself; \"You should act like an adult\"; \"Don't behave like a fool\"; \"What makes her do this way?\"",
"create or design, often in a certain way; \"Do my room in blue\"; \"I did this piece in wood to express my love for the ... | 9 | {"id": "br-j21:43:1", "sense_key": "do%2:41:04::", "split_group_id": "br-j21", "token_index": 1, "wordnet_version": "1.6"} |
To do this we must first [TARGET] show [/TARGET] that every line which meets \ g in a point P meets its image at P . | [
"establish the validity of something; \"This behavior shows his true nature\"",
"provide evidence for; \"The blood test showed that he was the father\"; \"Her behavior testified to her incompetence\"",
"indicate a place, direction, person, or thing; either spatially or figuratively; \"I showed the customer the ... | 1 | {"id": "br-j21:43:6", "sense_key": "show%2:32:00::", "split_group_id": "br-j21", "token_index": 6, "wordnet_version": "1.6"} |
To do this we must first show that every line which [TARGET] meets [/TARGET] \ g in a point P meets its image at P . | [
"contend against an opponent in a sport, game, or battle; \"Princeton plays Yale this weekend\"; \"Charlie likes to play Mary\"",
"fill or meet a want or need",
"be in contact with",
"get or come together; \"the two lines meet here\"",
"meet; \"I'll probably see you at the meeting\"; \"How nice to see you a... | 13 | {"id": "br-j21:43:11", "sense_key": "meet%2:42:02::", "split_group_id": "br-j21", "token_index": 11, "wordnet_version": "1.6"} |
To do this we must first show that every line which meets \ g in a point P [TARGET] meets [/TARGET] its image at P . | [
"contend against an opponent in a sport, game, or battle; \"Princeton plays Yale this weekend\"; \"Charlie likes to play Mary\"",
"fill or meet a want or need",
"be in contact with",
"get or come together; \"the two lines meet here\"",
"meet; \"I'll probably see you at the meeting\"; \"How nice to see you a... | 13 | {"id": "br-j21:43:18", "sense_key": "meet%2:42:02::", "split_group_id": "br-j21", "token_index": 18, "wordnet_version": "1.6"} |
To [TARGET] see [/TARGET] this , consider a general pencil of lines containing a general secant of \ G . | [
"consider or deem to be; regard; \"She views this quite differently from me\"; \"I consider her to be shallow\"",
"perceive mentally, as of an idea; \"Now I see!\"; \"I just can't see your point\"",
"get to know or become aware of; \"I learned that she has two grown-up children\"; \"I see that you have been pro... | 1 | {"id": "br-j21:44:1", "sense_key": "see%2:31:01::", "split_group_id": "br-j21", "token_index": 1, "wordnet_version": "1.6"} |
To see this , [TARGET] consider [/TARGET] a general pencil of lines containing a general secant of \ G . | [
"consider or deem to be; regard; \"She views this quite differently from me\"; \"I consider her to be shallow\"",
"consider, as of an example; \"Take the case of China\"; \"Consider the following case\"",
"judge or regard; look upon; judge; \"I think he is very smart\"; \"I believe her to be very smart\"; \"I t... | 1 | {"id": "br-j21:44:4", "sense_key": "consider%2:31:01::", "split_group_id": "br-j21", "token_index": 4, "wordnet_version": "1.6"} |
To see this , consider a general pencil of lines [TARGET] containing [/TARGET] a general secant of \ G . | [
"hold back, as of a danger or an enemy; check the expansion or influence of; \"Arrest the downward trend\"; \"Check the growth of communism in SE Asia\"; \"Contain the rebel movement\"",
"lessen the intensity of; temper; hold in restraint; hold or keep within limits; \"moderate your alcohol intake\" \"hold your t... | 2 | {"id": "br-j21:44:10", "sense_key": "contain%2:42:00::", "split_group_id": "br-j21", "token_index": 10, "wordnet_version": "1.6"} |
By ( 1 ) , the image of this pencil [TARGET] is [/TARGET] a ruled surface of order * * f which is met by the plane of the pencil in a curve , C , of order * * f . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 8 | {"id": "br-j21:45:9", "sense_key": "be%2:42:06::", "split_group_id": "br-j21", "token_index": 9, "wordnet_version": "1.6"} |
By ( 1 ) , the image of this pencil is a ruled surface of order * * f which is [TARGET] met [/TARGET] by the plane of the pencil in a curve , C , of order * * f . | [
"contend against an opponent in a sport, game, or battle; \"Princeton plays Yale this weekend\"; \"Charlie likes to play Mary\"",
"fill or meet a want or need",
"be in contact with",
"get or come together; \"the two lines meet here\"",
"meet; \"I'll probably see you at the meeting\"; \"How nice to see you a... | 13 | {"id": "br-j21:45:20", "sense_key": "meet%2:42:02::", "split_group_id": "br-j21", "token_index": 20, "wordnet_version": "1.6"} |
On C there [TARGET] is [/TARGET] a * * f correspondence in which the * * f points cut from C by a general line , l , of the pencil correspond to the point of intersection of the image of l and the plane of the pencil . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 7 | {"id": "br-j21:46:3", "sense_key": "be%2:42:05::", "split_group_id": "br-j21", "token_index": 3, "wordnet_version": "1.6"} |
On C there is a * * f correspondence in which the * * f points [TARGET] cut [/TARGET] from C by a general line , l , of the pencil correspond to the point of intersection of the image of l and the plane of the pencil . | [
"have grow through the gums; \"The baby cut a tooth\"",
"grow through the gums; \"The new tooth is cutting\"",
"cease, stop: \"cut the noise\"; \"We had to cut short the conversation\"",
"weed out unwanted or unnecessary things; \"We had to lose weight, so we cut the sugar from our diet\"",
"lessen the stre... | 33 | {"id": "br-j21:46:15", "sense_key": "cut%2:38:08::", "split_group_id": "br-j21", "token_index": 15, "wordnet_version": "1.6"} |
On C there is a * * f correspondence in which the * * f points cut from C by a general line , l , of the pencil [TARGET] correspond [/TARGET] to the point of intersection of the image of l and the plane of the pencil . | [
"exchange messages; \"My Russian pen pal and I have been corresponding for several years\"",
"be compatible, similar or consistent; coincide in their characteristics; \"The two stories don't agree in many details\"; \"The handwriting checks with the signature on the check\"",
"take the place of",
"be equivale... | 1 | {"id": "br-j21:46:28", "sense_key": "correspond%2:42:00::", "split_group_id": "br-j21", "token_index": 28, "wordnet_version": "1.6"} |
Since C [TARGET] is [/TARGET] rational , this correspondence has k coincidences , each of which implies a line of the pencil which meets its image . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 5 | {"id": "br-j21:47:2", "sense_key": "be%2:42:03::", "split_group_id": "br-j21", "token_index": 2, "wordnet_version": "1.6"} |
Since C is rational , this correspondence [TARGET] has [/TARGET] k coincidences , each of which implies a line of the pencil which meets its image . | [
"give birth (to a newborn); \"My wife had twins yesterday!\"",
"suffer from; be ill with; \"She has arthritis\"",
"of injuries and illnesses: \"She suffered a fracture in the accident\"; \"He had an insulin shock after eating three candy bars\"; \"She got a bruise on her leg\"; \"He got his arm broken in the sc... | 17 | {"id": "br-j21:47:7", "sense_key": "have%2:42:00::", "split_group_id": "br-j21", "token_index": 7, "wordnet_version": "1.6"} |
Since C is rational , this correspondence has k coincidences , each of which [TARGET] implies [/TARGET] a line of the pencil which meets its image . | [
"express or state indirectly",
"suggest as a logically necessary consequence; in logic",
"have as a logical consequence; \"The water shortage means that we have to stop taking long showers\"",
"have as a necessary feature or consequence; entail; \"This decision involves many changes\"",
"suggest that someon... | 2 | {"id": "br-j21:47:13", "sense_key": "imply%2:42:00::", "split_group_id": "br-j21", "token_index": 13, "wordnet_version": "1.6"} |
Since C is rational , this correspondence has k coincidences , each of which implies a line of the pencil which [TARGET] meets [/TARGET] its image . | [
"contend against an opponent in a sport, game, or battle; \"Princeton plays Yale this weekend\"; \"Charlie likes to play Mary\"",
"fill or meet a want or need",
"be in contact with",
"get or come together; \"the two lines meet here\"",
"meet; \"I'll probably see you at the meeting\"; \"How nice to see you a... | 13 | {"id": "br-j21:47:20", "sense_key": "meet%2:42:02::", "split_group_id": "br-j21", "token_index": 20, "wordnet_version": "1.6"} |
However , since the pencil [TARGET] contains [/TARGET] a secant of \ g it actually contains only * * f singular lines . | [
"hold back, as of a danger or an enemy; check the expansion or influence of; \"Arrest the downward trend\"; \"Check the growth of communism in SE Asia\"; \"Contain the rebel movement\"",
"lessen the intensity of; temper; hold in restraint; hold or keep within limits; \"moderate your alcohol intake\" \"hold your t... | 2 | {"id": "br-j21:48:5", "sense_key": "contain%2:42:00::", "split_group_id": "br-j21", "token_index": 5, "wordnet_version": "1.6"} |
However , since the pencil contains a secant of \ g it actually [TARGET] contains [/TARGET] only * * f singular lines . | [
"hold back, as of a danger or an enemy; check the expansion or influence of; \"Arrest the downward trend\"; \"Check the growth of communism in SE Asia\"; \"Contain the rebel movement\"",
"lessen the intensity of; temper; hold in restraint; hold or keep within limits; \"moderate your alcohol intake\" \"hold your t... | 2 | {"id": "br-j21:48:13", "sense_key": "contain%2:42:00::", "split_group_id": "br-j21", "token_index": 13, "wordnet_version": "1.6"} |
To [TARGET] avoid [/TARGET] this contradiction it is necessary that C be composite , with the secant of \ g and a curve of order * * f as components . | [
"stay clear from; keep away from; keep out of the way of someone or something; \"Her former friends now avoid her\"",
"refrain from certain foods of beverages; \"I keep off drugs\"; \"During Ramadan, Muslims avoid tobacco during the day\"",
"declare invalid; \"The contract was annulled\"; \"avoid a plea\"",
"... | 3 | {"id": "br-j21:49:1", "sense_key": "avoid%2:41:01::", "split_group_id": "br-j21", "token_index": 1, "wordnet_version": "1.6"} |
To avoid this contradiction it [TARGET] is [/TARGET] necessary that C be composite , with the secant of \ g and a curve of order * * f as components . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 5 | {"id": "br-j21:49:5", "sense_key": "be%2:42:03::", "split_group_id": "br-j21", "token_index": 5, "wordnet_version": "1.6"} |
To avoid this contradiction it is necessary that C [TARGET] be [/TARGET] composite , with the secant of \ g and a curve of order * * f as components . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 5 | {"id": "br-j21:49:9", "sense_key": "be%2:42:03::", "split_group_id": "br-j21", "token_index": 9, "wordnet_version": "1.6"} |
Thus it [TARGET] follows [/TARGET] that the secants of \ g are all invariant . | [
"behave in accordance or in agreement with; \"Follow a pattern\"; \"Follow my example\"",
"keep informed; \"He kept up on his country's foreign policies\"",
"keep to: \"Stick to your principles\"; \"stick to the diet\"",
"follow, discover, or ascertain the course of development of something; \"We must follow ... | 23 | {"id": "br-j21:50:2", "sense_key": "follow%2:42:05::", "split_group_id": "br-j21", "token_index": 2, "wordnet_version": "1.6"} |
Thus it follows that the secants of \ g [TARGET] are [/TARGET] all invariant . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 5 | {"id": "br-j21:50:9", "sense_key": "be%2:42:03::", "split_group_id": "br-j21", "token_index": 9, "wordnet_version": "1.6"} |
But if this [TARGET] is [/TARGET] the case , then an arbitrary pencil of lines having a point , P , of \ g as vertex is transformed into a ruled surface of order * * f having * * f generators concurrent at P . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 8 | {"id": "br-j21:51:3", "sense_key": "be%2:42:06::", "split_group_id": "br-j21", "token_index": 3, "wordnet_version": "1.6"} |
But if this is the case , then an arbitrary pencil of lines [TARGET] having [/TARGET] a point , P , of \ g as vertex is transformed into a ruled surface of order * * f having * * f generators concurrent at P . | [
"give birth (to a newborn); \"My wife had twins yesterday!\"",
"suffer from; be ill with; \"She has arthritis\"",
"of injuries and illnesses: \"She suffered a fracture in the accident\"; \"He had an insulin shock after eating three candy bars\"; \"She got a bruise on her leg\"; \"He got his arm broken in the sc... | 17 | {"id": "br-j21:51:13", "sense_key": "have%2:42:00::", "split_group_id": "br-j21", "token_index": 13, "wordnet_version": "1.6"} |
But if this is the case , then an arbitrary pencil of lines having a point , P , of \ g as vertex is [TARGET] transformed [/TARGET] into a ruled surface of order * * f having * * f generators concurrent at P . | [
"change or alter in form, appearance, or nature; \"This experience transformed her completely\"; \"She transformed the clay into a beautiful sculpture\"",
"change from one form or medium into another; \"Braque translated collage into oil\"",
"subject to a mathematical transformation",
"change in outward struc... | 2 | {"id": "br-j21:51:25", "sense_key": "transform%2:30:02::", "split_group_id": "br-j21", "token_index": 25, "wordnet_version": "1.6"} |
But if this is the case , then an arbitrary pencil of lines having a point , P , of \ g as vertex is transformed into a ruled surface of order * * f [TARGET] having [/TARGET] * * f generators concurrent at P . | [
"give birth (to a newborn); \"My wife had twins yesterday!\"",
"suffer from; be ill with; \"She has arthritis\"",
"of injuries and illnesses: \"She suffered a fracture in the accident\"; \"He had an insulin shock after eating three candy bars\"; \"She got a bruise on her leg\"; \"He got his arm broken in the sc... | 10 | {"id": "br-j21:51:35", "sense_key": "have%2:40:00::", "split_group_id": "br-j21", "token_index": 35, "wordnet_version": "1.6"} |
Since a ruled surface of order n with n concurrent generators [TARGET] is [/TARGET] necessarily a cone , it follows finally that every line through a point , P , of \ g meets its image at P , as asserted . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 8 | {"id": "br-j21:52:11", "sense_key": "be%2:42:06::", "split_group_id": "br-j21", "token_index": 11, "wordnet_version": "1.6"} |
Since a ruled surface of order n with n concurrent generators is necessarily a cone , it [TARGET] follows [/TARGET] finally that every line through a point , P , of \ g meets its image at P , as asserted . | [
"behave in accordance or in agreement with; \"Follow a pattern\"; \"Follow my example\"",
"keep informed; \"He kept up on his country's foreign policies\"",
"keep to: \"Stick to your principles\"; \"stick to the diet\"",
"follow, discover, or ascertain the course of development of something; \"We must follow ... | 23 | {"id": "br-j21:52:17", "sense_key": "follow%2:42:05::", "split_group_id": "br-j21", "token_index": 17, "wordnet_version": "1.6"} |
Since a ruled surface of order n with n concurrent generators is necessarily a cone , it follows finally that every line through a point , P , of \ g [TARGET] meets [/TARGET] its image at P , as asserted . | [
"contend against an opponent in a sport, game, or battle; \"Princeton plays Yale this weekend\"; \"Charlie likes to play Mary\"",
"fill or meet a want or need",
"be in contact with",
"get or come together; \"the two lines meet here\"",
"meet; \"I'll probably see you at the meeting\"; \"How nice to see you a... | 13 | {"id": "br-j21:52:31", "sense_key": "meet%2:42:02::", "split_group_id": "br-j21", "token_index": 31, "wordnet_version": "1.6"} |
Since a ruled surface of order n with n concurrent generators is necessarily a cone , it follows finally that every line through a point , P , of \ g meets its image at P , as [TARGET] asserted [/TARGET] . | [
"assert to be true; \"The letter asserts a free society\"",
"to declare or affirm as true: \"Before God I swear I am innocent.\"",
"state categorically",
"insist on having one's opinions and rights recognized; \"Women should assert themselves more!\""
] | 2 | {"id": "br-j21:52:38", "sense_key": "assert%2:32:01::", "split_group_id": "br-j21", "token_index": 38, "wordnet_version": "1.6"} |
Now [TARGET] consider [/TARGET] the transformation of the lines of a bundle with vertex , P , on \ g which is effected by the involution as a whole . | [
"consider or deem to be; regard; \"She views this quite differently from me\"; \"I consider her to be shallow\"",
"consider, as of an example; \"Take the case of China\"; \"Consider the following case\"",
"judge or regard; look upon; judge; \"I think he is very smart\"; \"I believe her to be very smart\"; \"I t... | 1 | {"id": "br-j21:53:1", "sense_key": "consider%2:31:01::", "split_group_id": "br-j21", "token_index": 1, "wordnet_version": "1.6"} |
Now consider the transformation of the lines of a bundle with vertex , P , on \ g which is [TARGET] effected [/TARGET] by the involution as a whole . | [
"cause to happen or occur; \"The scientists set up a shockwave\"",
"act so as to bring about; \"effect a change\"; \"carry out a reform\""
] | 0 | {"id": "br-j21:53:20", "sense_key": "effect%2:36:00::", "split_group_id": "br-j21", "token_index": 20, "wordnet_version": "1.6"} |
From the preceding remarks , it [TARGET] is [/TARGET] clear that such a bundle is transformed into itself in an involutorial fashion . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 5 | {"id": "br-j21:54:6", "sense_key": "be%2:42:03::", "split_group_id": "br-j21", "token_index": 6, "wordnet_version": "1.6"} |
From the preceding remarks , it is clear that such a bundle is [TARGET] transformed [/TARGET] into itself in an involutorial fashion . | [
"change or alter in form, appearance, or nature; \"This experience transformed her completely\"; \"She transformed the clay into a beautiful sculpture\"",
"change from one form or medium into another; \"Braque translated collage into oil\"",
"subject to a mathematical transformation",
"change in outward struc... | 2 | {"id": "br-j21:54:13", "sense_key": "transform%2:30:02::", "split_group_id": "br-j21", "token_index": 13, "wordnet_version": "1.6"} |
Moreover , in this involution there [TARGET] is [/TARGET] a cone of invariant lines of order * * f , namely the cone of secants of \ g which pass through P . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 7 | {"id": "br-j21:55:5", "sense_key": "be%2:42:05::", "split_group_id": "br-j21", "token_index": 5, "wordnet_version": "1.6"} |
Moreover , in this involution there is a cone of invariant lines of order * * f , namely the cone of secants of \ g which [TARGET] pass [/TARGET] through P . | [
"eliminate from the body; \"Pass a kidney stone\"",
"come to pass; occur: \"What is happening?\"; \"The meeting took place off without an incidence\"; \"Nothing occurred that seemed important\"",
"disappear gradually; as of emotions, for example; \"The pain eventually passed off\"",
"grant authorization or cl... | 24 | {"id": "br-j21:55:26", "sense_key": "pass%2:42:08::", "split_group_id": "br-j21", "token_index": 26, "wordnet_version": "1.6"} |
Hence it [TARGET] follows [/TARGET] that the involution within the bundle must be a perspective de Jonquieres involution of order * * f and the invariant locus must have a multiple line of multiplicity either * * f or * * f . | [
"behave in accordance or in agreement with; \"Follow a pattern\"; \"Follow my example\"",
"keep informed; \"He kept up on his country's foreign policies\"",
"keep to: \"Stick to your principles\"; \"stick to the diet\"",
"follow, discover, or ascertain the course of development of something; \"We must follow ... | 23 | {"id": "br-j21:56:2", "sense_key": "follow%2:42:05::", "split_group_id": "br-j21", "token_index": 2, "wordnet_version": "1.6"} |
Hence it follows that the involution within the bundle must [TARGET] be [/TARGET] a perspective de Jonquieres involution of order * * f and the invariant locus must have a multiple line of multiplicity either * * f or * * f . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 8 | {"id": "br-j21:56:10", "sense_key": "be%2:42:06::", "split_group_id": "br-j21", "token_index": 10, "wordnet_version": "1.6"} |
Hence it follows that the involution within the bundle must be a perspective de Jonquieres involution of order * * f and the invariant locus must [TARGET] have [/TARGET] a multiple line of multiplicity either * * f or * * f . | [
"give birth (to a newborn); \"My wife had twins yesterday!\"",
"suffer from; be ill with; \"She has arthritis\"",
"of injuries and illnesses: \"She suffered a fracture in the accident\"; \"He had an insulin shock after eating three candy bars\"; \"She got a bruise on her leg\"; \"He got his arm broken in the sc... | 17 | {"id": "br-j21:56:26", "sense_key": "have%2:42:00::", "split_group_id": "br-j21", "token_index": 26, "wordnet_version": "1.6"} |
The first possibility [TARGET] requires [/TARGET] that there be a line through P which meets \ g in * * f points ; the second requires that there be a line through P which meets \ g in * * f points . | [
"make someone do something",
"consider obligatory; request and expect; \"We require our secretary to be on time\"; \"Aren't we asking too much of these children?\" \"I expect my students to arrive in time for their lessons\"",
"have need of: \"This piano wants the attention of a competent tuner\"",
"require a... | 3 | {"id": "br-j21:57:3", "sense_key": "require%2:42:00::", "split_group_id": "br-j21", "token_index": 3, "wordnet_version": "1.6"} |
The first possibility requires that there be a line through P which [TARGET] meets [/TARGET] \ g in * * f points ; the second requires that there be a line through P which meets \ g in * * f points . | [
"contend against an opponent in a sport, game, or battle; \"Princeton plays Yale this weekend\"; \"Charlie likes to play Mary\"",
"fill or meet a want or need",
"be in contact with",
"get or come together; \"the two lines meet here\"",
"meet; \"I'll probably see you at the meeting\"; \"How nice to see you a... | 13 | {"id": "br-j21:57:12", "sense_key": "meet%2:42:02::", "split_group_id": "br-j21", "token_index": 12, "wordnet_version": "1.6"} |
The first possibility requires that there be a line through P which meets \ g in * * f points ; the second [TARGET] requires [/TARGET] that there be a line through P which meets \ g in * * f points . | [
"make someone do something",
"consider obligatory; request and expect; \"We require our secretary to be on time\"; \"Aren't we asking too much of these children?\" \"I expect my students to arrive in time for their lessons\"",
"have need of: \"This piano wants the attention of a competent tuner\"",
"require a... | 3 | {"id": "br-j21:57:23", "sense_key": "require%2:42:00::", "split_group_id": "br-j21", "token_index": 23, "wordnet_version": "1.6"} |
The first possibility requires that there be a line through P which meets \ g in * * f points ; the second requires that there be a line through P which [TARGET] meets [/TARGET] \ g in * * f points . | [
"contend against an opponent in a sport, game, or battle; \"Princeton plays Yale this weekend\"; \"Charlie likes to play Mary\"",
"fill or meet a want or need",
"be in contact with",
"get or come together; \"the two lines meet here\"",
"meet; \"I'll probably see you at the meeting\"; \"How nice to see you a... | 13 | {"id": "br-j21:57:32", "sense_key": "meet%2:42:02::", "split_group_id": "br-j21", "token_index": 32, "wordnet_version": "1.6"} |
In each case , lines of the bundles are [TARGET] transformed [/TARGET] by involutions within the pencils they determine with the multiple secant . | [
"change or alter in form, appearance, or nature; \"This experience transformed her completely\"; \"She transformed the clay into a beautiful sculpture\"",
"change from one form or medium into another; \"Braque translated collage into oil\"",
"subject to a mathematical transformation",
"change in outward struc... | 2 | {"id": "br-j21:58:9", "sense_key": "transform%2:30:02::", "split_group_id": "br-j21", "token_index": 9, "wordnet_version": "1.6"} |
In each case , lines of the bundles are transformed by involutions within the pencils they [TARGET] determine [/TARGET] with the multiple secant . | [
"reach, make, or come to a decision about something; \"We finally decided after lengthy deliberations\"",
"fix conclusively or authoritatively; \"set the rules\"",
"shape or influence; give direction to; \"experience often determines ability\"",
"fix in scope; fix the boundaries of; the tree determines the bo... | 3 | {"id": "br-j21:58:16", "sense_key": "determine%2:31:03::", "split_group_id": "br-j21", "token_index": 16, "wordnet_version": "1.6"} |
In the first case the fixed elements within each pencil [TARGET] are [/TARGET] the multiple secant and the line joining the vertex , P , to the intersection of \ g and the plane of the pencil which does not lie on the multiple secant . | [
"spend or use time: \"I may be an hour\"",
"work in a specific place, with a specific subject, or in a specific function; \"He is a herpetologist; \"She is our resident philosopher\"; \"She works as a waitress to put herself through law school\"",
"have an existence, be extant; \"Is there a God?\"",
"have lif... | 8 | {"id": "br-j21:59:10", "sense_key": "be%2:42:06::", "split_group_id": "br-j21", "token_index": 10, "wordnet_version": "1.6"} |
In the first case the fixed elements within each pencil are the multiple secant and the line [TARGET] joining [/TARGET] the vertex , P , to the intersection of \ g and the plane of the pencil which does not lie on the multiple secant . | [
"make contact or come together; \"The two roads join here\"",
"cause to become joined or linked",
"become part of; become a member of a group or organization; \"He joined the Communist Party as a young man\"",
"come into the company of; \"She joined him for a drink\"",
"be or become joined or united or link... | 1 | {"id": "br-j21:59:17", "sense_key": "join%2:35:01::", "split_group_id": "br-j21", "token_index": 17, "wordnet_version": "1.6"} |
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