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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ABC is equal ABCD alſo angle ABC angle ACB angle BAC arch baſe baſe BC becauſe the angle biſe&t caſe cauſe centre circle ABC circumference cofine conſequently demonſtrated deſcribed diameter diſtance equal angles equiangular equimultiples Euclid exterior angle fides figure fimilar firſt fore given ſtraight line greater half the ſum inſcribed join leſs Let ABC likewiſe magnitudes meaſure muſt oppoſite P R O parallel parallelogram parallelopiped paſs paſſes perpendicular plane angles priſm PROB propoſition Q. E. D. PROP radius rectangle contained rectilineal remaining angle right angles ſaid ſame manner ſame multiple ſame number ſame ratio ſame reaſon ſecond ſection ſegment ſhall be equal ſides ſolid angle ſome ſphere ſpherical triangle ſquare ſquare of AC ſuperficies tangent THEOR theſe thoſe triangle triangle ABC uſe 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.