| Science - 1844 - 434 pages
...proposition, too, would follow the converse of the first one, if ever the sum differed from 180". PROP. III. **The three angles of every triangle are equal to' two right angles.** B ' Let ABC be any equilateral trlanglfe ; ./\ / \ bisect its angles, which obviously will {[ •£... | |
| Euclides - 1845 - 544 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. Join AC, BD. And because... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...XXII. THKOR. — The opposite angles of any quadrilateral figure described in a circle, J are together **equal to two right angles. Let ABCD be a quadrilateral figure in the circle ABCD;** If in the first diagram, CE were produced to meet AB, the first case might be proved in a similar manner.... | |
| Plato - Atheism - 1845 - 460 pages
...say it is compelled to affirm, and does affirm this, with the same confidence as the proposition that **the three angles of every triangle are equal to two right angles,** or that two bodies cannot occupy the same space. Even this, notwithstanding it lies at the foundation... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 332 pages
...PROP. XXII. THEOR. The opposite angles of any quadrilateral figure described in a circle, are together **equal to two right angles. Let ABCD be a quadrilateral figure in the circle ABCD ; any** its opposite angles are together equal to two right angles. Join AC, BD. The angle CAB is equal (21.... | |
| Euclides - 1846 - 292 pages
...semicircle, is less than a right angle. Lastly, because ABCD is a quadrilateral figure in a circle, **any two of its opposite angles are together equal to two right angles** (3. 22) ; therefore the angles ABC, ADC are together equal to two right angles : But ABC is less than... | |
| Edward Shaw - Masonry - 1846 - 342 pages
...straight lines AF and BD, and consequently making the angle at G equal to the angle F А С ; and since **the three angles of every triangle are equal to two right angles,** and since the angles FA С, С AB, BAE, are also equal to two right angles, and since F А С is equal... | |
| David Benedict - Baptists - 1848 - 1026 pages
...not a head for the philosophy of language; and 1 say this with as liltle bad leeling as I say that **the three angles of every triangle are equal to two right angles.** " That Mr. President Beecher will be immersed in. one of the great American rivers, is now very improbable... | |
| Euclid, Thomas Tate - 1849 - 120 pages
...of any quadrilateral figure inscribed in a circle, are together equal to two right angles. LetABCobe **a quadrilateral figure in the circle ABCD; any two...because the three angles of every triangle are equal** (i. 32.) to two right angles, the three angles of the triangle CAB, viz. the angles CAB, ABC, BCA,... | |
| Elias Loomis - Conic sections - 1849 - 252 pages
...the sixth part of four right angles (Prop. II., Sch. 1), or the third part of two right angles. Also, **because the three angles of every triangle are equal to two right angles, the** two angles OAB, OBA are together equal to two thirds of two jj^—^C right angles; and since AO is... | |
| |