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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. "
Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ... - Page 71
by Euclid - 1845 - 199 pages
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The Edinburgh New Philosophical Journal: Exhibiting a View of the ..., Volume 36

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 {[ •...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

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...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

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....
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Plato Contra Atheos

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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

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....
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

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...
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Practical Masonry, Or, A Theoretical and Operative Treatise of Building ...

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...
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A General History of the Baptist Denomination in America and Other Parts of ...

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...
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The first three books of Euclid's Elements of geometry, with theorems and ...

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,...
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Elements of Geometry and Conic Sections

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...
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