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 TrigonometryLippincott, Grambo & Company, 1854 - 317 σελίδες |
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Σελίδα 108
... magnitudes are continual proportionals , the ratio of the first to the third is said to be duplicate of the ratio of the first to the second " Thus , if A be to B as B to C , the ratio of A to C is said to be duplicate of the ratio of A ...
... magnitudes are continual proportionals , the ratio of the first to the third is said to be duplicate of the ratio of the first to the second " Thus , if A be to B as B to C , the ratio of A to C is said to be duplicate of the ratio of A ...
Σελίδα 109
... magnitudes are taken two and two . 20. Ex æquali , from equality ; this term is used simply by itself , when the first magnitude is to the second of the first rank , as the first to the second of the other rank ; and as the second is to ...
... magnitudes are taken two and two . 20. Ex æquali , from equality ; this term is used simply by itself , when the first magnitude is to the second of the first rank , as the first to the second of the other rank ; and as the second is to ...
Σελίδα 110
... magnitude by any number , a multiple of the same mag- nitude by any number be added , the sum will be the same ... magnitudes contain the second as often as there are units in a certain number , and if the second contain the third ...
... magnitude by any number , a multiple of the same mag- nitude by any number be added , the sum will be the same ... magnitudes contain the second as often as there are units in a certain number , and if the second contain the third ...
Σελίδα 111
... magnitude taken from the first is of a magnitude taken from the other ; the remainder is the same multiple of the remainder , that the whole is of the whole Let mA and mB be any equimultiples of the two magnitudes A and B , of which A ...
... magnitude taken from the first is of a magnitude taken from the other ; the remainder is the same multiple of the remainder , that the whole is of the whole Let mA and mB be any equimultiples of the two magnitudes A and B , of which A ...
Σελίδα 112
... magnitudes be proportionals , they are proportionals also when taken inversely . If A B C : D , then also B : A :: D : C. : Let mA and mC be any equimultiples of A and C ; nB and nD any equi- multiples of B and D. Then , because A : B ...
... magnitudes be proportionals , they are proportionals also when taken inversely . If A B C : D , then also B : A :: D : C. : Let mA and mC be any equimultiples of A and C ; nB and nD any equi- multiples of B and D. Then , because A : B ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal 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 PROB PROP proportional 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 touches the circle triangle ABC triangle DEF wherefore