Euclid's Elements of geometry, books i. ii. iii. iv1862 |
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Αποτελέσματα 1 - 5 από τα 45.
Σελίδα 6
... shown that BC is equal to BG . 6. Therefore AL and BC are each of them equal to BG . 7. But things which are equal to the same thing are equal to one another , therefore AL is equal to BC . ( ax . 1. ) Conclusion . Therefore from the ...
... shown that BC is equal to BG . 6. Therefore AL and BC are each of them equal to BG . 7. But things which are equal to the same thing are equal to one another , therefore AL is equal to BC . ( ax . 1. ) Conclusion . Therefore from the ...
Σελίδα 8
... shown . PROPOSITION 5. - THEOREM . the The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon other side of the base shall also be equal . ( References - Prop . I ...
... shown . PROPOSITION 5. - THEOREM . the The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon other side of the base shall also be equal . ( References - Prop . I ...
Σελίδα 9
... shown . Corollary . Hence every equilateral triangle is also equi- angular . PROPOSITION 6. - THEOREM . If two angles of a triangle be equal to one another , the sides also which subtend , or are opposite to , the equal angles , shall ...
... shown . Corollary . Hence every equilateral triangle is also equi- angular . PROPOSITION 6. - THEOREM . If two angles of a triangle be equal to one another , the sides also which subtend , or are opposite to , the equal angles , shall ...
Σελίδα 10
... . Much more then is the angle BDČ greater than BCD . * Q. E. D. is an abbreviation for quod erat demonstrandum , that is , " which was to be shown or proved . " 6. Again , because BC is assumed to be equal 10 EUCLID'S ELEMENTS .
... . Much more then is the angle BDČ greater than BCD . * Q. E. D. is an abbreviation for quod erat demonstrandum , that is , " which was to be shown or proved . " 6. Again , because BC is assumed to be equal 10 EUCLID'S ELEMENTS .
Σελίδα 11
... shown to be greater than the angle BCD . ( dem . 5. ) 9. Therefore the angle BDC is both equal to , and greater than the same angle BCD , which is impossible . Case II . - Let the vertex of one of the triangles fall within the other ...
... shown to be greater than the angle BCD . ( dem . 5. ) 9. Therefore the angle BDC is both equal to , and greater than the same angle BCD , which is impossible . Case II . - Let the vertex of one of the triangles fall within the other ...
Συχνά εμφανιζόμενοι όροι και φράσεις
AB is equal AC and CB adjacent angles angle ABC angle AGH angle BAC angle BCD angle EAB angle EDF angle equal angles CBA base BC BC is equal bisected circle ABC circumference Conclusion Conclusion.-Therefore const Construction.-1 Demonstration.-1 describe the circle diameter double equal angles equal to CD equiangular exterior angle given circle given point given rectilineal angle given straight line Given.-Let ABCD gnomon greater Hypothesis inscribed interior and opposite isosceles triangle less opposite angle parallel to CD parallelogram perpendicular point F produced Q. E. D. PROPOSITION rectangle AB BC rectangle AE rectangle contained rectilineal figure References-Prop remaining angle required to describe right angles segment semicircle Sequence side BC square on AC straight line AC straight line drawn touches the circle triangle ABC triangle DEF twice the rectangle
Δημοφιλή αποσπάσματα
Σελίδα 25 - 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.
Σελίδα 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Σελίδα 99 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 4 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Σελίδα 66 - ... 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...
Σελίδα 65 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Σελίδα 32 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 58 - 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...
Σελίδα 88 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Σελίδα 33 - The straight lines which join the extremities of two equal and parallel straight lines towards the same parts, are also themselves equal and parallel.