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 vii
... demonstrating more easily some of the properties of parallel lines . In the third Book , the remarks con- cerning the angles made by a straight line , and the circumference of a circle , are left out , as tending to perplex one who has ...
... demonstrating more easily some of the properties of parallel lines . In the third Book , the remarks con- cerning the angles made by a straight line , and the circumference of a circle , are left out , as tending to perplex one who has ...
Σελίδα xv
... demonstrate that any two sides of a triangle are greater than the third ; it may be replied , that this is no doubt a truth which , without proof , most men will be inclined to admit ; but are we for that reason to account it of no ...
... demonstrate that any two sides of a triangle are greater than the third ; it may be replied , that this is no doubt a truth which , without proof , most men will be inclined to admit ; but are we for that reason to account it of no ...
Σελίδα 24
... demonstrated . PROP . V. THEOR . The angles at the base of an Isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall also be equal . Let ABC be an isosceles ...
... demonstrated . PROP . V. THEOR . The angles at the base of an Isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall also be equal . Let ABC be an isosceles ...
Σελίδα 25
... demonstrated , that the whole angle ABG is equal to the whole ACF , and the part CBG , to the part BCF the remaining angle ABC is therefore equal to the remaining angle ACB , which are the angles at the base of the triangle ABC : And it ...
... demonstrated , that the whole angle ABG is equal to the whole ACF , and the part CBG , to the part BCF the remaining angle ABC is therefore equal to the remaining angle ACB , which are the angles at the base of the triangle ABC : And it ...
Σελίδα 26
... demonstrated to be greater than it ; which is impossible . But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ECD ...
... demonstrated to be greater than it ; which is impossible . But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ECD ...
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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