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 páginas |
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Página 40
... proved to be equal to GHD ; therefore EGB is likewise equal to GHD ; add to each of these the angle BGH ; therefore the angles EGB . BGH are equal to the angles BGH , GHD ; but EGB , BGH are equal ( 13. 1. ) to two right angles ...
... proved to be equal to GHD ; therefore EGB is likewise equal to GHD ; add to each of these the angle BGH ; therefore the angles EGB . BGH are equal to the angles BGH , GHD ; but EGB , BGH are equal ( 13. 1. ) to two right angles ...
Página 87
... ; therefore the angles DBF , DBE , being likewise equal ( 13. 1. ) to two right angles , are equal to the angles BAD , BCD ; and DBF has E B F been proved equal to BAD : therefore the remaining angle OF GEOMETRY . BOOK III . 87.
... ; therefore the angles DBF , DBE , being likewise equal ( 13. 1. ) to two right angles , are equal to the angles BAD , BCD ; and DBF has E B F been proved equal to BAD : therefore the remaining angle OF GEOMETRY . BOOK III . 87.
Página 88
... proved equal to BAD : therefore the remaining angle DBE is equal to the angle BCD in the alternate segment of the circle . Wherefore , if a straight line , & c . Q. E. D. PROP . XXXIII . PROB . Upon a given straight line to describe a ...
... proved equal to BAD : therefore the remaining angle DBE is equal to the angle BCD in the alternate segment of the circle . Wherefore , if a straight line , & c . Q. E. D. PROP . XXXIII . PROB . Upon a given straight line to describe a ...
Página 115
... proved , A : C :: B : C , and inversely ( A. 5. ) , C : A :: C : B. Therefore , & c . Q. E. D. PROP . VIII . THEOR . Of unequal magnitudes , the greater has a greater ratio to the same than the less has ; and the same magnitude has a ...
... proved , A : C :: B : C , and inversely ( A. 5. ) , C : A :: C : B. Therefore , & c . Q. E. D. PROP . VIII . THEOR . Of unequal magnitudes , the greater has a greater ratio to the same than the less has ; and the same magnitude has a ...
Página 118
... proved , that if A = C , B = D ; and if AZC , BLD . Therefore , & c . Q. E. D. PROP . XV . THEOR . f Magnitudes have the same ratio to one another which their equimultiples have . If A and B be two magnitudes , and m any number , A : B ...
... proved , that if A = C , B = D ; and if AZC , BLD . Therefore , & c . Q. E. D. PROP . XV . THEOR . f Magnitudes have the same ratio to one another which their equimultiples have . If A and B be two magnitudes , and m any number , A : B ...
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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