The school Euclid: comprising the first four books, by A.K. Isbister1862 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 21.
Σελίδα 8
... likewise the angles contained by these sides equal to each other : then they shall likewise have their bases , or third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz ...
... likewise the angles contained by these sides equal to each other : then they shall likewise have their bases , or third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz ...
Σελίδα 12
... likewise those which are terminated in the other extremity . ( References Prop . 1. 5 ; ax . 9. ) If it be possible , let there be two triangles , ACB , ADB , upon the same base AB , and upon the same side of it , which have their sides ...
... likewise those which are terminated in the other extremity . ( References Prop . 1. 5 ; ax . 9. ) If it be possible , let there be two triangles , ACB , ADB , upon the same base AB , and upon the same side of it , which have their sides ...
Σελίδα 14
... likewise be greater than the angle 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 DB , therefore the angle BDC must be equal to the angle BCD ...
... likewise be greater than the angle 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 DB , therefore the angle BDC must be equal to the angle BCD ...
Σελίδα 15
... likewise their sides which are terminated in the other extremity ; but this is impossible . ( 1. 7. ) Therefore , if the base BC coincides with the base EF , the sides BA , AC , cannot but coincide with the sides ED , DF ; wherefore the ...
... likewise their sides which are terminated in the other extremity ; but this is impossible . ( 1. 7. ) Therefore , if the base BC coincides with the base EF , the sides BA , AC , cannot but coincide with the sides ED , DF ; wherefore the ...
Σελίδα 24
... likewise the angles CAB , ABC . Therefore any two angles , & c . Q. E. D. PROP . XVIII . — THEOREM . The greater side of every triangle is opposite to the greater angle ; i.e. , in any triangle , if one side be greater than another ...
... likewise the angles CAB , ABC . Therefore any two angles , & c . Q. E. D. PROP . XVIII . — THEOREM . The greater side of every triangle is opposite to the greater angle ; i.e. , in any triangle , if one side be greater than another ...
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.