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 TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 109
... fourth , but the third to the fourth a greater ratio than the fifth has to the sixth ; the first has also to the second a greater ratio than the fifth has to the sixth . If A B C D ; but C : D7E : F ; then also , A : B7E : F ...
... fourth , but the third to the fourth a greater ratio than the fifth has to the sixth ; the first has also to the second a greater ratio than the fifth has to the sixth . If A B C D ; but C : D7E : F ; then also , A : B7E : F ...
Página 110
... fourth , has to the fourth , the first will have to the second the same ratio which the third has to the fourth . If A + B B :: C + D : D , then by division A : B :: C : D. : Take mA and nB any multiples of A and B , by the numbers m ...
... fourth , has to the fourth , the first will have to the second the same ratio which the third has to the fourth . If A + B B :: C + D : D , then by division A : B :: C : D. : Take mA and nB any multiples of A and B , by the numbers m ...
Página 111
... fourth . If A : B : C : D , by conversion , A : A - B :: C : C - D . : For , since A B :: Č : D , by division ( 17 ... fourth is greater than the sixth ; if equal , equal ; and if less , less . If there be three magnitudes , A , B , and ...
... fourth . If A : B : C : D , by conversion , A : A - B :: C : C - D . : For , since A B :: Č : D , by division ( 17 ... fourth is greater than the sixth ; if equal , equal ; and if less , less . If there be three magnitudes , A , B , and ...
Página 112
... fourth is greater than the sixth ; if equal , equal ; and if less , less . If there be three magnitudes , A , B , C , and other three , D , E , and F , such that A : B :: E : F , and B : C :: D : E ; if A7C , D7F ; if A = C , D = F ...
... fourth is greater than the sixth ; if equal , equal ; and if less , less . If there be three magnitudes , A , B , C , and other three , D , E , and F , such that A : B :: E : F , and B : C :: D : E ; if A7C , D7F ; if A = C , D = F ...
Página 113
... fourth ; and the fifth to the second , the same ratio which the sixth has to the fourth ; the first and fifth together , shall have to the second , the same ratio which the third and sixth together , have to the fourth . Let A B C D ...
... fourth ; and the fifth to the second , the same ratio which the sixth has to the fourth ; the first and fifth together , shall have to the second , the same ratio which the third and sixth together , have to the fourth . Let A B C D ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore