Elements of Geometry; Containing the First Six Books of Euclid ...For Bell & Bradfute, 1814 - 461 Seiten |
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Seite viii
... reason , because , to measure the length of the simplest of all the curves which Geometry treatest of and the space contained within it , are problems that cer- tainly belong to the elements of the science , es- pecially as they are not ...
... reason , because , to measure the length of the simplest of all the curves which Geometry treatest of and the space contained within it , are problems that cer- tainly belong to the elements of the science , es- pecially as they are not ...
Seite 39
... reason , the exterior angle CEB of the tri- angle ABE is greater than BAC ; and it has been de- monstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than Book I the angle BAC . Therefore ...
... reason , the exterior angle CEB of the tri- angle ABE is greater than BAC ; and it has been de- monstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than Book I the angle BAC . Therefore ...
Seite 53
... reason EF is Book I. equal to BC ; wherefore AD is equal to EF ; and DE C b b 1. Ax . c 2. or 3 . is common ; therefore the whole , or the remainder , AE is equal to the whole , or the remainder DF ; now AB Ax . is also equal to DC ...
... reason EF is Book I. equal to BC ; wherefore AD is equal to EF ; and DE C b b 1. Ax . c 2. or 3 . is common ; therefore the whole , or the remainder , AE is equal to the whole , or the remainder DF ; now AB Ax . is also equal to DC ...
Seite 54
... reason , the parallelogram EFGH is equal to the same EBCH : Therefore also the parallelogram ABCD is equal to EFGH . Wherefore , parallelograms , & c . Q. E. D. a 51. 1 . b 35. 1 . c 54. 1 . d 7. Ax . PROP . XXXVII . THEOR . Triangles ...
... reason , the parallelogram EFGH is equal to the same EBCH : Therefore also the parallelogram ABCD is equal to EFGH . Wherefore , parallelograms , & c . Q. E. D. a 51. 1 . b 35. 1 . c 54. 1 . d 7. Ax . PROP . XXXVII . THEOR . Triangles ...
Seite 58
... reason , the triangle KGC is equal to the triangle KFC . Then , be- cause the triangle AEK is equal to the triangle AHK , and the triangle KGC to the triangle KFC ; the tri- angle AEK , together with the triangle KGC is equal to the ...
... reason , the triangle KGC is equal to the triangle KFC . Then , be- cause the triangle AEK is equal to the triangle AHK , and the triangle KGC to the triangle KFC ; the tri- angle AEK , together with the triangle KGC is equal to the ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC arch AC base BC bisected Book centre circle ABC circumference cosine cylinder definition demonstrated described diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles GEOMETRY given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram perpendicular polygon prism PROB proportional proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle SPHERICAL TRIGONOMETRY straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore