Euclidian Geometry |
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Page v
... parallels ; for a theorem is assumed as self - evident which certainly requires proof as much as those which are made to depend upon it . To avoid this difficulty a Lemma has been introduced which , while it rests on an axiomatic basis ...
... parallels ; for a theorem is assumed as self - evident which certainly requires proof as much as those which are made to depend upon it . To avoid this difficulty a Lemma has been introduced which , while it rests on an axiomatic basis ...
Page vi
... parallel is that suggested by the literal meaning of the word : thus the conception of a paral- lelogram is not that of a figure whose opposite sides will never meet however far they may be produced in either direction , but rather that ...
... parallel is that suggested by the literal meaning of the word : thus the conception of a paral- lelogram is not that of a figure whose opposite sides will never meet however far they may be produced in either direction , but rather that ...
Page x
... ...... 6 B 17 C Parallels . Lemma 20 ... 21 ..31 n Р 27 , 28 9 ........ 22 ( 29 ) ( 30 ) r 23 .33 I. 22 24 .32 I. 25 25 ( 269 ) m ......... II . 9 , 10 Contact of Os . 2 7 5 , 6 .... 7 8 .. IO ..29 9 . ............ 13 ...
... ...... 6 B 17 C Parallels . Lemma 20 ... 21 ..31 n Р 27 , 28 9 ........ 22 ( 29 ) ( 30 ) r 23 .33 I. 22 24 .32 I. 25 25 ( 269 ) m ......... II . 9 , 10 Contact of Os . 2 7 5 , 6 .... 7 8 .. IO ..29 9 . ............ 13 ...
Page xi
... Parallel lines . Parallel planes , 9 10 31 13 14 F 18 14 16 G .25 A 10 , 15 B 17 13 I2 14 Comp . of Os . 12 .... XII . 2 , & c . Comp . of Ls . 13 .. ( 33 ) Planes to planes . II ... XII . I 15 18 16 19 Solid angles . 17 18 18 20 21 ...
... Parallel lines . Parallel planes , 9 10 31 13 14 F 18 14 16 G .25 A 10 , 15 B 17 13 I2 14 Comp . of Os . 12 .... XII . 2 , & c . Comp . of Ls . 13 .. ( 33 ) Planes to planes . II ... XII . I 15 18 16 19 Solid angles . 17 18 18 20 21 ...
Page xv
... parallel . + together with . = equal to . > greater than . < less than . ... because . ... therefore . : is to . The object aimed at is merely to place before the student the various steps of an argument in a more succinct form by ...
... parallel . + together with . = equal to . > greater than . < less than . ... because . ... therefore . : is to . The object aimed at is merely to place before the student the various steps of an argument in a more succinct form by ...
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Common terms and phrases
Algebra Arithmetic base BEGINNERS Cambridge centre chord Christ's College circumference cloth Conic Sections Crown 8vo Describe a circle diagonals diameter divided ELEMENTARY TREATISE English equiangular equilateral Euclid Examples Extra fcap GEOMETRY given angle given circle given point given straight line Grammar greater H Let Hence inscribed intersecting isosceles triangle John's College Latin Let ABC line bisecting locus magnitudes Mathematical meet Owens College parallel parallelogram perimeter perpendicular plane PROBLEM produced Professor proportional PROPOSITION radius ratio rect rectangle rectangle contained rectilineal figure regular polygon render respectively revised rhombus right angles Schools Second Edition segment Similarly squares on AC straight line joining student tangent THEOREM TRIGONOMETRY twice rectangle twice the squares Uppingham School vertex
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Page 157 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
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