Euclid's Elements of geometry, books i. ii. iii. iv1862 |
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Side 72
... pass through the centre , it shall cut it at right angles ; and conversely , if it cut it at right angles , it shall bisect it . ( References - Prop . I. 5 , 8 , 26 ; III . 1. ) Hypothesis I. Let ABC be a circle , and let CD , a ...
... pass through the centre , it shall cut it at right angles ; and conversely , if it cut it at right angles , it shall bisect it . ( References - Prop . I. 5 , 8 , 26 ; III . 1. ) Hypothesis I. Let ABC be a circle , and let CD , a ...
Side 73
... pass through the centre . If Sequence . - AC , BD , shall not bisect one another . one of the lines pass through the centre , it is plain that it cannot be bisected by the other , which does not pass through the centre . Hypothesis II ...
... pass through the centre . If Sequence . - AC , BD , shall not bisect one another . one of the lines pass through the centre , it is plain that it cannot be bisected by the other , which does not pass through the centre . Hypothesis II ...
Side 75
... passes through the centre , is always greater than one more remote ; and from the same point there can be drawn to the circumference two straight lines , and only two , which are equal to one another , one on each side of the diameter ...
... passes through the centre , is always greater than one more remote ; and from the same point there can be drawn to the circumference two straight lines , and only two , which are equal to one another , one on each side of the diameter ...
Side 76
... passes through the centre ; of those which fall on the concave circumference , the greatest is that which passes through the centre , and of the rest , that which is nearer to the one passing through the centre is always greater than ...
... passes through the centre ; of those which fall on the concave circumference , the greatest is that which passes through the centre , and of the rest , that which is nearer to the one passing through the centre is always greater than ...
Side 77
... passes through the centre . Sequence . - 1 . Of the lines which fall on the concave part of the circumference AEFC , the greatest shall be DA , which passes through the centre , and the nearer to it shall be greater than the more remote ...
... passes through the centre . Sequence . - 1 . Of the lines which fall on the concave part of the circumference AEFC , the greatest shall be DA , which passes through the centre , and the nearer to it shall be greater than the more remote ...
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.