The school Euclid: comprising the first four books, by A.K. Isbister1862 |
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Σελίδα 25
... likewise greater than the angle ACB ; wherefore much more is the angle ABC greater than the angle ACB . Therefore the greater side , & c . Q. E. D. PROP . XIX . - THEOREM . The greater angle of every triangle is subtended by the greater ...
... likewise greater than the angle ACB ; wherefore much more is the angle ABC greater than the angle ACB . Therefore the greater side , & c . Q. E. D. PROP . XIX . - THEOREM . The greater angle of every triangle is subtended by the greater ...
Σελίδα 33
... likewise in this case the other sides shall be equal , AC to DF , and BC to EF ; and also the third angle BAC to the third angle EDF . A D АД B H C E F CONSTRUCTION For if BC be not equal to EF , C 3 PROP . XXVI . ] 333 THE SCHOOL ...
... likewise in this case the other sides shall be equal , AC to DF , and BC to EF ; and also the third angle BAC to the third angle EDF . A D АД B H C E F CONSTRUCTION For if BC be not equal to EF , C 3 PROP . XXVI . ] 333 THE SCHOOL ...
Σελίδα 37
... likewise the two interior angles upon the same side together equal to two right angles . ( References - Prop . I. 13 , 15 ; ax . I. 2 , 4 , 12. ) Let the right line EF , fall on the parallel lines AB , CD . Then the alternate angle AGĦ ...
... likewise the two interior angles upon the same side together equal to two right angles . ( References - Prop . I. 13 , 15 ; ax . I. 2 , 4 , 12. ) Let the right line EF , fall on the parallel lines AB , CD . Then the alternate angle AGĦ ...
Σελίδα 53
... likewise to the angle D , therefore the angle ABM is equal to the angle D. Wherefore the parallelogram LB is applied to the straight line AB , and is equal to the triangle C , and has the angle ABM equal to the angle D. Q. E. F. PROP ...
... likewise to the angle D , therefore the angle ABM is equal to the angle D. Wherefore the parallelogram LB is applied to the straight line AB , and is equal to the triangle C , and has the angle ABM equal to the angle D. Q. E. F. PROP ...
Σελίδα 55
... Likewise all its angles are right angles ; for , since the straight line AD meets the parallels AB , DE , therefore the angles BAD , ADE are equal to two right angles ; ( 1. 29 ) but BAD is a right angle ; ( constr . ) therefore also ...
... Likewise all its angles are right angles ; for , since the straight line AD meets the parallels AB , DE , therefore the angles BAD , ADE are equal to two right angles ; ( 1. 29 ) but BAD is a right angle ; ( constr . ) therefore also ...
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.