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 142
... similar to the triangle FGL ABE has to FGL the duplicate ratio ( 19. 6. ) of that which the side BE has to the side GL for the same reason , the triangle BEC has to GLH the duplicate ratio of that which BE has to GL : therefore , as the ...
... similar to the triangle FGL ABE has to FGL the duplicate ratio ( 19. 6. ) of that which the side BE has to the side GL for the same reason , the triangle BEC has to GLH the duplicate ratio of that which BE has to GL : therefore , as the ...
Σελίδα 143
... similar , and similarly described rectilineal figure upon the second . COR . 3. Because all squares are similar figures , the ratio of any two squares to one another is the same with the duplicate ratio of their sides ; and hence , also ...
... similar , and similarly described rectilineal figure upon the second . COR . 3. Because all squares are similar figures , the ratio of any two squares to one another is the same with the duplicate ratio of their sides ; and hence , also ...
Σελίδα 144
... similar rectilineal figures MF , NH , in like manner : the rectilineal figure KAB is to LCD , as MF to NH . To AB ... similar , and similarly situated to ei- A K B D 合合口 M E N G R ther of the figures MF , NH : then , because that as ...
... similar rectilineal figures MF , NH , in like manner : the rectilineal figure KAB is to LCD , as MF to NH . To AB ... similar , and similarly situated to ei- A K B D 合合口 M E N G R ther of the figures MF , NH : then , because that as ...
Σελίδα 145
... similar , both to the whole parallogram ABCD , and to one another . Because DC , GF are parallels , the angle ADC is equal ( 29. 1. ) to the angle AGF for the same reason , because BC , EF are parallels , the angle ABC is equal to the ...
... similar , both to the whole parallogram ABCD , and to one another . Because DC , GF are parallels , the angle ADC is equal ( 29. 1. ) to the angle AGF for the same reason , because BC , EF are parallels , the angle ABC is equal to the ...
Σελίδα 146
... similar to one another ( def . 1. 6. ) for the same reason , the parallelogram ABCD is similar to the parallelogram FHCK . Wherefore each of the parallelograms , GE , KH is similar to DB : but rectilineal figures which are similar to ...
... similar to one another ( def . 1. 6. ) for the same reason , the parallelogram ABCD is similar to the parallelogram FHCK . Wherefore each of the parallelograms , GE , KH is similar to DB : but rectilineal figures which are similar to ...
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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