Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical TrigonometryE. Duyckinck, and George Long, 1824 - 333 σελίδες |
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Σελίδα 45
... reason . the parallelogram EFGH is equal to the same EBCH : Therefore also the parallelo- gram ABCD is equal to EFGH . Wherefore , parallelograms , & c . Q. E. D. Triangles upon PROP . XXXVII . THEOR . the same base , and between the ...
... reason . the parallelogram EFGH is equal to the same EBCH : Therefore also the parallelo- gram ABCD is equal to EFGH . Wherefore , parallelograms , & c . Q. E. D. Triangles upon PROP . XXXVII . THEOR . the same base , and between the ...
Σελίδα 48
... reason , the triangle KGC is equal to the triangle KFC . Then , because the tri- angle AEK is equal to the triangle AHK , and the triangle KGC to the triangle KFC ; the triangle AEK , together with the triangle KGC is equal to the ...
... reason , the triangle KGC is equal to the triangle KFC . Then , because the tri- angle AEK is equal to the triangle AHK , and the triangle KGC to the triangle KFC ; the triangle AEK , together with the triangle KGC is equal to the ...
Σελίδα 51
... reason , AB and AH are in the same straight line . Now because the angle DBC is equal to the angle FBA , each of them being a right angle , adding to each the angle ABC , the whole angle DBA will be equal ( 2. Ax . ) to the whole FBC ...
... reason , AB and AH are in the same straight line . Now because the angle DBC is equal to the angle FBA , each of them being a right angle , adding to each the angle ABC , the whole angle DBA will be equal ( 2. Ax . ) to the whole FBC ...
Σελίδα 55
... CGKB are also right angles ( Cor . 46. 1. ) . Wherefore CGKB is a square , it is upon the side CB . For the same reason HF also is a square , and D F E and it is upon the side HG , which is equal OF GEOMETRY . BOOK II . 55.
... CGKB are also right angles ( Cor . 46. 1. ) . Wherefore CGKB is a square , it is upon the side CB . For the same reason HF also is a square , and D F E and it is upon the side HG , which is equal OF GEOMETRY . BOOK II . 55.
Σελίδα 58
... reason , PR is equal to RO ; and because CB is equal to BD , and GK to KN , the rectangles CK and BN are equal , as also the rectangles GR and RN : But CK is equal ( 43. 1. ) to RN , because they are the complements of the parallelogram ...
... reason , PR is equal to RO ; and because CB is equal to BD , and GK to KN , the rectangles CK and BN are equal , as also the rectangles GR and RN : But CK is equal ( 43. 1. ) to RN , because they are the complements of the parallelogram ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals 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 straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore