The school Euclid: comprising the first four books, by A.K. Isbister1862 |
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Resultat 6-10 av 63
Side 7
... greater of two given straight lines to cut off a part equal to the less . ( References - Prop . 1. 2 ; def . 15 ; post . 3 ; ax . 1. ) Let B and C be the given straight lines , of which AB is greater than C. It is required to cut off ...
... greater of two given straight lines to cut off a part equal to the less . ( References - Prop . 1. 2 ; def . 15 ; post . 3 ; ax . 1. ) Let B and C be the given straight lines , of which AB is greater than C. It is required to cut off ...
Side 8
... greater of two straight lines , a part AE has been cut off equal to C , the less . Which was to be done . PROP . IV . - THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each ; and have ...
... greater of two straight lines , a part AE has been cut off equal to C , the less . Which was to be done . PROP . IV . - THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each ; and have ...
Side 10
... greater , cut off AG equal to AF , the less , ( 1. 3 ) and join FC , GB . DEMONSTRATION Because AF is equal to AG ; ( constr . ) and AB to AC ; ( hypoth . ) the two sides FA , AC , are equal to the two GA , AB , each to each , and they ...
... greater , cut off AG equal to AF , the less , ( 1. 3 ) and join FC , GB . DEMONSTRATION Because AF is equal to AG ; ( constr . ) and AB to AC ; ( hypoth . ) the two sides FA , AC , are equal to the two GA , AB , each to each , and they ...
Side 12
... greater than the other . Let AB be the greater ; and from it cut off DB equal to AC , the less , ( 1. 3. ) and join DC . DEMONSTRATION Then in the triangles DBC , ACB , because DB is assumed to be equal to AC , and BC is common to both ...
... greater than the other . Let AB be the greater ; and from it cut off DB equal to AC , the less , ( 1. 3. ) and join DC . DEMONSTRATION Then in the triangles DBC , ACB , because DB is assumed to be equal to AC , and BC is common to both ...
Side 13
... 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 . Again , because in the triangle BCD , CB is assumed to be equal to BD ...
... 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 . Again , because in the triangle BCD , CB is assumed to be equal to BD ...
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The school Euclid: comprising the first four books, by A.K. Isbister Euclides Uten tilgangsbegrensning - 1863 |
The School Euclid: Comprising the First Four Books, Chiefly from the Text of ... A. K. Isbister Ingen forhåndsvisning tilgjengelig - 2009 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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...
Side 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.
Side 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...
Side 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.
Side 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...
Side 43 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Side 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.
Side 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.
Side 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.