Euclid's Elements of geometry, books i. ii. iii. iv1862 |
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Σελίδα 4
... proved , as a theorem . A problem proposes something to be done , such as the con- struction of a figure . A theorem makes an assertion , the truth of which it proposes to demonstrate . A postulate is a problem so simple that it is ...
... proved , as a theorem . A problem proposes something to be done , such as the con- struction of a figure . A theorem makes an assertion , the truth of which it proposes to demonstrate . A postulate is a problem so simple that it is ...
Σελίδα 7
... because the straight line AC is equal to DF . ( hypothesis . ) * Q . E. F. is an abbreviation for quod erat faciendum , that is , " which was to be done . " 6. But the point B was proved to coincide with BOOK I. 7 PROP . 4 .
... because the straight line AC is equal to DF . ( hypothesis . ) * Q . E. F. is an abbreviation for quod erat faciendum , that is , " which was to be done . " 6. But the point B was proved to coincide with BOOK I. 7 PROP . 4 .
Σελίδα 8
Euclides. 6. But the point B was proved to coincide with the point E. 7. Therefore the base BC shall coincide with the base EF . 8. Because the point B coinciding with E , and C with F , if the base BC do not coincide with the base EF ...
Euclides. 6. But the point B was proved to coincide with the point E. 7. Therefore the base BC shall coincide with the base EF . 8. Because the point B coinciding with E , and C with F , if the base BC do not coincide with the base EF ...
Σελίδα 9
... proved to be equal to GB . ( ax . 3. ) 8. Therefore the two sides BF , FC , are equal to the two sides CG , GB , each to each . 9. And the angle BFC was proved equal to the angle CGB . 10. Therefore the triangles BFC , CGB , are equal ...
... proved to be equal to GB . ( ax . 3. ) 8. Therefore the two sides BF , FC , are equal to the two sides CG , GB , each to each . 9. And the angle BFC was proved equal to the angle CGB . 10. Therefore the triangles BFC , CGB , are equal ...
Σελίδα 10
... 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 .
... 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 .
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.