Euclidian Geometry |
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Page xvi
... whole is equal to the sum of its parts . If equals be added to equals the wholes are equal . If equals be taken from equals the remainders are equal . If equals be added to unequals the wholes are unequal . If equals be taken from ...
... whole is equal to the sum of its parts . If equals be added to equals the wholes are equal . If equals be taken from equals the remainders are equal . If equals be added to unequals the wholes are unequal . If equals be taken from ...
Page 8
... whole = EHF is the whole EDF , and .. BAC is = LEDF . ( ii ) If HD passes through one extremity of 8 STRAIGHT LINES , ANGLES AND TRIANGLES .
... whole = EHF is the whole EDF , and .. BAC is = LEDF . ( ii ) If HD passes through one extremity of 8 STRAIGHT LINES , ANGLES AND TRIANGLES .
Page 42
... whole ACK is the two angles ABC , BAC together . Now to each of these equals add the ACB ; = .. the two angles ACK , ACB are together the three Ls of the △ ABC ' ; but the two angles ACK , ACB are together = two rights ; = ( 1.9 ) ...
... whole ACK is the two angles ABC , BAC together . Now to each of these equals add the ACB ; = .. the two angles ACK , ACB are together the three Ls of the △ ABC ' ; but the two angles ACK , ACB are together = two rights ; = ( 1.9 ) ...
Page 44
... whole Also ABC is the whole ADC . = ABD , △ ADB , and the side BD , are re- spectively CDB , CBD , and side BD ; ( 1.3 ) .. AS ABD , CDB are equal in all respects ; .. AB , AD , and BAD are respectively CD , CB , and BCD ...
... whole Also ABC is the whole ADC . = ABD , △ ADB , and the side BD , are re- spectively CDB , CBD , and side BD ; ( 1.3 ) .. AS ABD , CDB are equal in all respects ; .. AB , AD , and BAD are respectively CD , CB , and BCD ...
Page 56
... = ARGQ , and △ PQK = ^ NQK ; .. AS SGQ , PQK are together but the whole △ FGK is = = = as RGQ , NQK ; the △ HGK ; .. the remainder FQ is the remainder QH . PROPOSITION XXXV . In any right - angled triangle , 56 AREAS .
... = ARGQ , and △ PQK = ^ NQK ; .. AS SGQ , PQK are together but the whole △ FGK is = = = as RGQ , NQK ; the △ HGK ; .. the remainder FQ is the remainder QH . PROPOSITION XXXV . In any right - angled triangle , 56 AREAS .
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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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