The elements of Euclid: viz. the first six books, with the eleventh and twelfth. In which the corrections of Dr. Simson are generally adopted, but the errors overlooked by him are corrected, and the obscurities of his and other editions explained. Also some of Euclid's demonstrations are restored, others made shorter and more general, and several useful propositions are added. Together with elements of plane and spherical trigonometry, and a treatise on practical geometry
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ABCD angle ABC angle ACB angle BAC angles equal arch BC base BC BC is equal bisect centre circle ABC circumference cosine demonstrated desinition diameter draw E. D. PROP equal angles equal to AC equiangular equilateral equimultiples Euclid exterior angle faid fame altitude fame base fame manner fame multiple fame number fame plane fame ratio fame reason fame straight line fore frustum given straight line gnomon half the sum inches join less Let ABC line BC magnitudes meet parallel parallelogram parallelopiped perpendicular plane angles prism PROB proportionals proposition radius rectangle contained rectilineal sigure remaining angle right angles segment sides similar sine sirst solid angle spherical angle spherical triangle square of AC straight line AC supersicies tangent THEOR tiple touches the circle triangle ABC Wherefore
Page 30 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 13 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 30 - ... then shall the other sides be equal, each to each; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.
Page 72 - The diameter is the greatest straight line in a circle; and of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...
Page 57 - If then the sides of it, BE, ED are equal to one another, it is a square, and what was required is now done: But if they are not equal, produce one of them BE to F, and make EF equal to ED, and bisect BF in G : and from the centre G, at the distance GB, or GF, describe the semicircle...
Page 145 - AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off.
Page 48 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 35 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.