 | William Thomas Read - 1862 - 144 pages
...proved may be obtained, which shows them to be true for any triangle. • We know (by Eu. 1, 32), that the three angles of every triangle are equal to two right angles ; therefore those of ABC are equal to two right angles ; and since B = 90°, therefore A + C = 90°,... | |
 | Euclides - 1864 - 448 pages
...the circle ABCD. Then any two of its opposite angles shall together be equal to two right angles. c Join AC, BD. And because the three angles of every triangle are equal to two right angles, (I. 32.) the three angles of the triangle CAB, viz. the angles CAB, ABC, BCA, are equal to two right... | |
 | Euclides - 1864 - 262 pages
...XXII. THEOREM. The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles, Let ABCD be a quadrilateral figure in the circle ABCD. Then any two of its opposite angles shall together be equal to two right angles. .0 Join AC, BD. And... | |
 | Robert Potts - 1865 - 528 pages
...PROPOSITION XXn. THEOREM. The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles. Let ABCD be a quadrilateral figure in the circle AB CD. Then any two of its opposite angles shall together bfe equal to two right angles. Join AC, BD.... | |
 | Euclides - 1865 - 402 pages
...snall be together equal to two right angles. CONSTRUCTION Draw the diagonals AC and I)B. DEMONSTRATION Because the three angles of every triangle are equal to two right angles, (I. 32) the three angles of the triangle CAB, viz. the angles CAB, ABC, BCA, are equal to two right... | |
 | John Fry Heather - Mathematical instruments - 1866 - 228 pages
...the two angles HI A and '•* HA i ; and because the vertical angles AVH and IVE are equal, and that the three angles of every triangle are equal to two right angles, therefore the two angles VIE and s EH are, together, equal to the two angles AH v and HA i, and therefore... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...than a semicircle, is less than a right angle. And because ABCD is a quadrilateral figure in a circle, any two of its opposite angles are together equal to two right angles ; [III. 22. therefore the angles ABC, ADC are together equal to two right angles. But the angle ABC... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...a quadrilateral have two of its opposite sides parallel, and the two others equal but not parallel, any two of its opposite angles are together equal to two right 74. If a straight lino which joins the extremities of two equal straight lines, not parallel, make... | |
 | Robert Potts - 1868 - 434 pages
...circle A BCD. Then any two of its opposite angles shall together be equal to two right anglss. .0 Jam AC, BD. And because the three angles of every triangle are equal to two right angles, (I. 32.) the three angles of the triangle CAB, viz. the angles CAB, ABC, BCA, are equal to two right... | |
 | John Fry Heather - Drawing instruments - 1871 - 224 pages
...two interior angles H i A and HA i ; and because the vertical angles AVH and iv E are equal, and that the three angles of every triangle are equal to two right angles, therefore the two angles VIE and SEE are, together, equal to the two angles AH v and HA i, and therefore... | |
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The opposite angles of any quadrilateral figure described in a circle, are toe/ether equal to two right angles. Let ABCD be a quadrilateral figure in the circle ABCD : any two of its opposite angles are together equal to two right angles. 
