Euclid's Elements of geometry, books i. ii. iii. iv1862 |
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Side 18
... G , it may be proved that the angle BCG ( or its equal ACD ) , is greater than the angle ABC . Conclusion . - Therefore , if one side , & c . Q. E. D. PROPOSITION 17. - THEOREM . Any two angles of a 18 EUCLID'S ELEMENTS .
... G , it may be proved that the angle BCG ( or its equal ACD ) , is greater than the angle ABC . Conclusion . - Therefore , if one side , & c . Q. E. D. PROPOSITION 17. - THEOREM . Any two angles of a 18 EUCLID'S ELEMENTS .
Side 19
... proved that the angles BAC , ACB , as also the angles CAB , ABC , are together less than two right angles . Conclusion . Therefore , any two angles , & c . Q. E. D. PROPOSITION 18. - THEOREM . The greater side of every triangle is ...
... proved that the angles BAC , ACB , as also the angles CAB , ABC , are together less than two right angles . Conclusion . Therefore , any two angles , & c . Q. E. D. PROPOSITION 18. - THEOREM . The greater side of every triangle is ...
Side 20
... proved that AC is not equal to AB . 7. Therefore AC is greater than AB . Conclusion . Therefore , the greater angle , & c . Q. E. D. PROPOSITION 20. - THEOREM . Any two sides of a triangle are together greater than the third side ...
... proved that AC is not equal to AB . 7. Therefore AC is greater than AB . Conclusion . Therefore , the greater angle , & c . Q. E. D. PROPOSITION 20. - THEOREM . Any two sides of a triangle are together greater than the third side ...
Side 21
... proved that AB , BC , are greater than AC , and BC , CA , greater than AB . Conclusion . - Therefore , any two sides , & c . Q. E. D. PROPOSITION 21. - THEOREM . If from the ends of the side of a triangle there be drawn two straight ...
... proved that AB , BC , are greater than AC , and BC , CA , greater than AB . Conclusion . - Therefore , any two sides , & c . Q. E. D. PROPOSITION 21. - THEOREM . If from the ends of the side of a triangle there be drawn two straight ...
Side 24
... proved equal to BC ; 11. Therefore BC is greater than EF . Conclusion . Therefore , if two triangles , & c . Q. E. D. PROPOSITION 25. - THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each ...
... proved equal to BC ; 11. Therefore BC is greater than EF . Conclusion . Therefore , if two triangles , & c . Q. E. D. PROPOSITION 25. - THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 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...
Side 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...
Side 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.
Side 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.
Side 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...
Side 88 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Side 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.