The school Euclid: comprising the first four books, by A.K. Isbister1862 |
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Αποτελέσματα 6 - 10 από τα 100.
Σελίδα 10
... CONSTRUCTION E In BD take any point F , and from AE , the 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 ...
... CONSTRUCTION E In BD take any point F , and from AE , the 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 ...
Σελίδα 12
... CONSTRUCTION For , if AB be not equal to AC , one of them is 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 ...
... CONSTRUCTION For , if AB be not equal to AC , one of them is 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 ...
Σελίδα 13
... CONSTRUCTION Join the vertices C and D by the straight line CD . DEMONSTRATION Because , in the triangle ACD , AC is assumed to be equal to AD , therefore the angle ACD must be equal to the angle ADC ; ( 1 5 ) but the angle ACD is ...
... CONSTRUCTION Join the vertices C and D by the straight line CD . DEMONSTRATION Because , in the triangle ACD , AC is assumed to be equal to AD , therefore the angle ACD must be equal to the angle ADC ; ( 1 5 ) but the angle ACD is ...
Σελίδα 15
... angle . It is required to bisect it . B A А D E CONSTRUCTION Take any point D in AB , from AC cut off AE equal to AD , ( 1. 3 ) and join DE ; upon the side of it opposite to A , describe PROP . IX . ] 15 THE SCHOOL EUCLID .
... angle . It is required to bisect it . B A А D E CONSTRUCTION Take any point D in AB , from AC cut off AE equal to AD , ( 1. 3 ) and join DE ; upon the side of it opposite to A , describe PROP . IX . ] 15 THE SCHOOL EUCLID .
Σελίδα 16
... CONSTRUCTION Upon the straight line AB describe the equilateral triangle ABC , ( 1. 1 ) and bisect the angle ACB by the straight line CD . ( 1.9 . ) Then AB shall be divided into two equal parts in the point D. DEMONSTRATION Because AC ...
... CONSTRUCTION Upon the straight line AB describe the equilateral triangle ABC , ( 1. 1 ) and bisect the angle ACB by the straight line CD . ( 1.9 . ) Then AB shall be divided into two equal parts in the point D. DEMONSTRATION Because AC ...
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.