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 113
... fourth , and if any equimultiples whatever be taken of the first and third , and any whatever of the second and fourth ; the multiple of the first shall have the same ratio to the multiple of the second , that the multiple of the third ...
... fourth , and if any equimultiples whatever be taken of the first and third , and any whatever of the second and fourth ; the multiple of the first shall have the same ratio to the multiple of the second , that the multiple of the third ...
Σελίδα 114
... fourth ; the first is to the second as the third to the fourth . First , if mA , mB be equimultiples of the magnitudes A and B , mA : A :: mB : B. Take of mA and mB equimultiples by any number n ; and of A and B equimultiples by any ...
... fourth ; the first is to the second as the third to the fourth . First , if mA , mB be equimultiples of the magnitudes A and B , mA : A :: mB : B. Take of mA and mB equimultiples by any number n ; and of A and B equimultiples by any ...
Σελίδα 115
... fourth ; and if the first be a multiple or a part of the second , the third is the same multiple or the same part of the fourth . Let A B C : D , and first let A be a multiple of B , C is the same multiple of D , that is , if A = mB , C ...
... fourth ; and if the first be a multiple or a part of the second , the third is the same multiple or the same part of the fourth . Let A B C : D , and first let A be a multiple of B , C is the same multiple of D , that is , if A = mB , C ...
Σελίδα 117
... 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 ...
Σελίδα 118
... fourth ; if equal , equal ; and if less , less . : If A B C D ; then if A7C , B7D ; if A = C , B = D ; and if ALC ... fourth , has to the fourth , the first will have to the second the same ratio which the third has to the fourth . If A ...
... fourth ; if equal , equal ; and if less , less . : If A B C D ; then if A7C , B7D ; if A = C , B = D ; and if ALC ... fourth , has to the fourth , the first will have to the second the same ratio which the third has to the fourth . If A ...
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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