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 sider |
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Side 110
... magnitudes are continual proportionals , the ratio of the first to the fourth is said to be triplicate of the ratio ... magnitude of proportionals , so as that they continue still to be proportionals . XIV . Permutando , or alternando ...
... magnitudes are continual proportionals , the ratio of the first to the fourth is said to be triplicate of the ratio ... magnitude of proportionals , so as that they continue still to be proportionals . XIV . Permutando , or alternando ...
Side 111
... magnitudes are taken two and two . XX . 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 ...
... magnitudes are taken two and two . XX . 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 ...
Side 112
... magnitudes be equimultiples of as many others , each of each , what multiple soever any one of the first is of its part , the same multiple is the sum of all the first of the sum of all the rest . Let any number of magnitudes A , B ...
... magnitudes be equimultiples of as many others , each of each , what multiple soever any one of the first is of its part , the same multiple is the sum of all the first of the sum of all the rest . Let any number of magnitudes A , B ...
Side 113
... magnitude taken from the first is of a magnitude taken from the other ; the re- mainder 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 ...
... magnitude taken from the first is of a magnitude taken from the other ; the re- mainder 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 ...
Side 114
... 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 equimultiples 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 equimultiples of B and D. Then , because A : B ...
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Vanlige uttrykk og setninger
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