 | William Chauvenet - 1871 - 380 σελίδες
...CG+ DG = AH + DH + BF + CF, that is, BC. PROPOSITION XLV.— THEOREM. 102. Conversely, if the sum of two opposite sides of a quadrilateral is equal to the sum of the other two sides, the quadrilateral may be circumscribed about a circle. In the quadrilateral ABCD,... | |
 | Edward Olney - 1872 - 562 σελίδες
...— In any regular polygon, the ^ ^ sum of the perpendiculars let fall from the 7 10. If the sum of two opposite sides of a quadrilateral is equal to the sum of the other two opposite sides, a circle may be inscribed ill it SUG'S.— Bisect any two adjacent angles,... | |
 | William Chauvenet - 1872 - 382 σελίδες
...+ CG + DG = AH + DH + BF + CF, that is, PROPOSITION XLV.—THEOREM. 102. Conversely, if the sum of two opposite sides of a quadrilateral is equal to the sum of the other two sides, the quadrilateral may be circumscribed about a circle. In the quadrilateral ABCD,... | |
 | Edward Olney - 1872 - 102 σελίδες
...COR.—In any regular polygon, the FlG m sum of the perpendiculars let fall from the 710. If the sum of two opposite sides of a quadrilateral is equal to the sum of the other two opposite sides, a circle may be inscribed in it. SUo's. — Bisect any two adjacent angles,... | |
 | Edward Olney - 1872 - 96 σελίδες
...centre, is equal to the sum of those let fall from the vertices on the other side. 7 10. If the sum of two opposite sides of a quadrilateral is equal to the sum of the other two opposite sides, a circle may be inscribed in it. BUG'S. — Bisect any two adjacent angles,... | |
 | Aaron Schuyler - 1876 - 384 σελίδες
...; .-. ABCD is inscriptible. 185. Proposition III. — Theorem. GEOMETRY.— BOOK II. if the sum of two opposite sides of a quadrilateral is equal to the sum of the otlier two sides, the quadrilateral is circumscriptible. Let the circumscriptible quadrilateral ABDE... | |
 | Elias Loomis - 1877 - 458 σελίδες
...equations, we have • AF+BF+CH+DH=AE+DE+BG+CG; that is, AB+CD •= AD+BC. PROPOSITION V. 8. If the sum of two opposite sides of a quadrilateral is equal to the sum of the Other two sides, a circle can be inscribed within the quadrilateral. I.et ABCD be a quadrilateral,... | |
 | Edward Olney - 1883 - 352 σελίδες
...angles. Having proved the preceding, base the proof of this upon that. 3. Theorem.—// the sum of two opposite sides of a quadrilateral is equal to the sum of the other two opposite sides, show that a circle can be inscribed in the quadrilateral. 4. Theorem.—//... | |
 | William Ernest Johnson - 1889 - 574 σελίδες
...the inscribed circle is equal to half the difference between the two other sides. 10. If the sum of two opposite sides of a quadrilateral is equal to the sum of the two other opposite sides, a circle may be inscribed in the quadrilateral. 11. The angle which each... | |
 | George Washington Hull - 1897 - 408 σελίδες
...two circles tangent internally, the chords of the intercepted arcs are parallel. 568. If the sum of two opposite sides of a quadrilateral is equal to the sum of the other two sides, the quadrilateral may be circumscribed about a circle. 569. The centre of a circle... | |
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... is equal to the sum of the areas of the squares on the other two sides. 
