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 vi
... proportionals can be deduced by reasonings , which , at the same time that they are perfectly rigorous , are also simple and direct . As to the defects , the prolixness and ob- scurity , that have so often been complained of in the ...
... proportionals can be deduced by reasonings , which , at the same time that they are perfectly rigorous , are also simple and direct . As to the defects , the prolixness and ob- scurity , that have so often been complained of in the ...
Σελίδα 108
... proportionals , when the first has the same ratio to the second that the third has to the fourth ; and the third to ... proportionals , it is usual to " say that A is to B as C to D , and to write them thus , A : B :: " C : D , or thus ...
... proportionals , when the first has the same ratio to the second that the third has to the fourth ; and the third to ... proportionals , it is usual to " say that A is to B as C to D , and to write them thus , A : B :: " C : D , or thus ...
Σελίδα 109
... proportionals , the second is said to be a mean proportional between the other two . X. When there is any number of ... proportionals , the ratio of the first , to the third is said to be duplicate of the ratio of the first to the se ...
... proportionals , the second is said to be a mean proportional between the other two . X. When there is any number of ... proportionals , the ratio of the first , to the third is said to be duplicate of the ratio of the first to the se ...
Σελίδα 110
... proportionals ; the ratio of the first " to the fifth is called quadruplicate of the ratio of the first to the ... proportionals , the antecedent terms are called homologous to one another , as also the consequents to one another ...
... proportionals ; the ratio of the first " to the fifth is called quadruplicate of the ratio of the first to the ... proportionals , the antecedent terms are called homologous to one another , as also the consequents to one another ...
Σελίδα 111
... proportionals when taken two and two of each rank , and it is inferred , that the first is to the last of the first ... proportion . It is demonstrated in the 22d Prop . Book 5 . XXI . Ex æquali , in proportione perturbata , seu ...
... proportionals when taken two and two of each rank , and it is inferred , that the first is to the last of the first ... proportion . It is demonstrated in the 22d Prop . Book 5 . XXI . Ex æquali , in proportione perturbata , seu ...
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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