The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books : with Notes, an Appendix, and Exercises |
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Page i
... Third Edition . Crown 8vo . cloth . 58 . A Treatise on Spherical on Spherical Trigono- metry for the use of Colleges and Schools . Second Edition . Crown 8vo . cloth . 48. 6d . 8. A Treatise on Conic Sections . With numerous Examples ...
... Third Edition . Crown 8vo . cloth . 58 . A Treatise on Spherical on Spherical Trigono- metry for the use of Colleges and Schools . Second Edition . Crown 8vo . cloth . 48. 6d . 8. A Treatise on Conic Sections . With numerous Examples ...
Page ii
... Third Edition . Crown 8vo . cloth . IOS . 6d . 13. A History of the Progress of the Calculus of Variations during the Nineteenth Century . 8vo . cloth . 128 . 14. A History of the Mathematical Theory of Probability , from the time of ...
... Third Edition . Crown 8vo . cloth . IOS . 6d . 13. A History of the Progress of the Calculus of Variations during the Nineteenth Century . 8vo . cloth . 128 . 14. A History of the Mathematical Theory of Probability , from the time of ...
Page 9
... third sides equal ; and the two triangles shall be equal , and their other angles shall be equal , each to each , namely those to which the equal sides are opposite . Let ABC , DEF be two triangles which have the two sides AB , AC equal ...
... third sides equal ; and the two triangles shall be equal , and their other angles shall be equal , each to each , namely those to which the equal sides are opposite . Let ABC , DEF be two triangles which have the two sides AB , AC equal ...
Page 23
... third side . Let ABC be a triangle : any two sides of it are together greater than the third side ; namely , BA , AC greater than BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA to D , making AD equal to AC ...
... third side . Let ABC be a triangle : any two sides of it are together greater than the third side ; namely , BA , AC greater than BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA to D , making AD equal to AC ...
Page 24
... third side , the two sides BA , AE of the triangle ABE are greater than the side BE . To each of these add EC . Therefore BA , AC are greater than BE , EC . [ I. 20 . Again ; the two sides CE , ED of the triangle CED are greater than ...
... third side , the two sides BA , AE of the triangle ABE are greater than the side BE . To each of these add EC . Therefore BA , AC are greater than BE , EC . [ I. 20 . Again ; the two sides CE , ED of the triangle CED are greater than ...
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Common terms and phrases
ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore
Popular passages
Page 35 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Page 67 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle, is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle, Let ABC be an obtuse-angled triangle, having the obtuse angle...
Page 73 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.
Page 284 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 50 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Page 57 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Page 10 - 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 be equal.
Page 227 - If two straight lines be at right angles to the same plane, they shall be parallel to one another. Let the straight lines AB, CD be at right angles to the same plane : AB is parallel to CD.
Page 102 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Page 352 - Prove that the square on any straight line drawn from the vertex of an isosceles triangle to the base, is less than the square on a side of the triangle by the rectangle contained by the segments of the base : and conversely.