Euclidian Geometry |
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Page 5
... Let ABC be an isosceles △ , having the side AB = the side AC , then shall the ABC be = the A ACB ; also let the equal sides AB , AC be produced to G , H ; then shall GBC be = HCB . B For if the figure were taken up , re- versed , and ...
... Let ABC be an isosceles △ , having the side AB = the side AC , then shall the ABC be = the A ACB ; also let the equal sides AB , AC be produced to G , H ; then shall GBC be = HCB . B For if the figure were taken up , re- versed , and ...
Page 8
... Let the sides AB , BC , CA of the ABC be respec- tively equal to the sides DE , EF , FD of the A DEF . Then shall ... H. Join HD . B ( i ) If HD cuts EF . E D H · EH is = ED , . LEHD is = LEDH ; ( I. 2 ) and · . · FH is = FD , .. L ...
... Let the sides AB , BC , CA of the ABC be respec- tively equal to the sides DE , EF , FD of the A DEF . Then shall ... H. Join HD . B ( i ) If HD cuts EF . E D H · EH is = ED , . LEHD is = LEDH ; ( I. 2 ) and · . · FH is = FD , .. L ...
Page 14
... Let two intersecting straight lines form the four angles A , B , H , K. = Then shall the opposite angles A , B be one another . For if the figure were taken up , reversed , and placed so that each of the arms of H might fall along ...
... Let two intersecting straight lines form the four angles A , B , H , K. = Then shall the opposite angles A , B be one another . For if the figure were taken up , reversed , and placed so that each of the arms of H might fall along ...
Page 17
... Let ABC , GHK be two right angles , and let the ABC be applied to the GHK , so that B may fall on H , and BC along HK , then will BA fall along HG . For if it fell in any other direction , as HX , then from H there would be drawn two ...
... Let ABC , GHK be two right angles , and let the ABC be applied to the GHK , so that B may fall on H , and BC along HK , then will BA fall along HG . For if it fell in any other direction , as HX , then from H there would be drawn two ...
Page 22
... Let the side BC of △ ABC be produced to D. Then shall the ACD be > either of the S BAC , ABC . Bisect AC in E ; join BE and produce BE to F , making EF BE . H Join CF. Then , AE , EB are respectively CE , EF , = and △ AEB is = = CEF ...
... Let the side BC of △ ABC be produced to D. Then shall the ACD be > either of the S BAC , ABC . Bisect AC in E ; join BE and produce BE to F , making EF BE . H Join CF. Then , AE , EB are respectively CE , EF , = and △ AEB is = = CEF ...
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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...
Page 15 - ... and the principles on which the observations made with these instruments are treated for deduction of the distances and weights of the bo.iits of the Solar System, and of a few stars, omitting all minutiit of Elementary Class- Books — continued. formulcE, and all troublesome details of calculation.