The school Euclid: comprising the first four books, by A.K. Isbister1862 |
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Αποτελέσματα 6 - 10 από τα 100.
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 14
... triangle BCD , CB is assumed to be 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 ...
... triangle BCD , CB is assumed to be 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 ...
Σελίδα 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 ...
Σελίδα 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 ...
Άλλες εκδόσεις - Προβολή όλων
The School Euclid: Comprising the First Four Books, Chiefly from the Text of ... A. K. Isbister Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2009 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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...
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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...
Σελίδα 43 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.