The school Euclid: comprising the first four books, by A.K. Isbister1862 |
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Página 12
Euclides Alexander Kennedy Isbister. Let the triangle ABC have the angle ABC equal to the angle ACB . Then the side AB shall be equal to the side AC . A B -- CONSTRUCTION For , if AB be not equal to AC , one of them is greater than the ...
Euclides Alexander Kennedy Isbister. Let the triangle ABC have the angle ABC equal to the angle ACB . Then the side AB shall be equal to the side AC . A B -- CONSTRUCTION For , if AB be not equal to AC , one of them is greater than the ...
Página 13
... angle ACD must be equal to the angle ADC ; ( 1 5 ) but the angle ACD is greater than the angle BCD ; ( ax . 9 ) therefore the angle ADC must be greater also than BCD ; much more then must the angle BDC be greater than the angle BCD ...
... angle ACD must be equal to the angle ADC ; ( 1 5 ) but the angle ACD is greater than the angle BCD ; ( ax . 9 ) therefore the angle ADC must be greater also than BCD ; much more then must the angle BDC be greater than the angle BCD ...
Página 14
... equal to DB , therefore the angle BDC must be equal to the angle BCD ; ( 1.5 ) but BDC has been proved to be greater than BCD ; wherefore the angle BDC must be both equal to , and greater than , the angle BCD ; which is impossible ...
... equal to DB , therefore the angle BDC must be equal to the angle BCD ; ( 1.5 ) but BDC has been proved to be greater than BCD ; wherefore the angle BDC must be both equal to , and greater than , the angle BCD ; which is impossible ...
Página 15
... equal to EF , ( hyp . ) therefore the point C shall coincide with the point F ; wherefore BC coinciding with EF , BA ... angle BAC coincides with the angle EDF , and is equal to it . ( ax . 8. ) Therefore , if two triangles , & c ...
... equal to EF , ( hyp . ) therefore the point C shall coincide with the point F ; wherefore BC coinciding with EF , BA ... angle BAC coincides with the angle EDF , and is equal to it . ( ax . 8. ) Therefore , if two triangles , & c ...
Página 16
... angle DAF is equal to the angle EAF . ( 1. 8. ) Wherefore the given rectilineal angle BAC is bisected by the line AF . Q. E. F PROP . X.- PROBLEM . To bisect a given finite straight line , that is , to divide it into two equal parts ...
... angle DAF is equal to the angle EAF . ( 1. 8. ) Wherefore the given rectilineal angle BAC is bisected by the line AF . Q. E. F PROP . X.- PROBLEM . To bisect a given finite straight line , that is , to divide it into two equal parts ...
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The School Euclid: Comprising the First Four Books, Chiefly from the Text of ... A. K. Isbister Sin vista previa disponible - 2009 |
Términos y frases comunes
AB is equal adjacent angles alternate angles angle ABC angle AGH angle BAC angle BCD angle EAB angle EDF angle equal angles CBA base BC BC is equal circle ABC constr DEMONSTRATION describe the circle diameter double equal angles equal straight lines equal to BC equilateral and equiangular exterior angle given circle given rectilineal angle given straight line gnomon greater inscribed interior and opposite less Let ABC Let the straight opposite angles parallel to CD parallelogram pentagon perpendicular Q. E. D. PROP rectangle AE rectangle contained rectilineal figure References Prop References-Prop remaining angle required to describe right angles segment semicircle side BC square of AC straight line AB straight line AC THEOREM touches the circle triangle ABC triangle DEF twice the rectangle
Pasajes populares
Página 141 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Página 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.
Página 71 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of 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...
Página 33 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Página 61 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of...
Página 43 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Página 27 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.
Página 77 - An angle in a segment is the angle contained by two straight lines drawn from any point in the circumference of the segment to the extremities of the straight line which is the base of the segment.
Página 15 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles.