The Elements of GeometryMacmillan, 1886 - 366 páginas |
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Página xi
... Inscribed angles PAGE 129 , 130 · • 130-132 . 132 , 133 · · 117 . 117 • " 117 . 117 III . Angles in Segments . secants . · • 134-138 117 . 117 118 IV . Tangents . • 118 • 389-402 . 119 defined . Properties of tangents • . • • · 138 139 ...
... Inscribed angles PAGE 129 , 130 · • 130-132 . 132 , 133 · · 117 . 117 • " 117 . 117 III . Angles in Segments . secants . · • 134-138 117 . 117 118 IV . Tangents . • 118 • 389-402 . 119 defined . Properties of tangents • . • • · 138 139 ...
Página xii
... inscribed hexagon equals radius PAGE 159 ures . 438 . Isoperimetric defined . 159 427-435 . To inscribe and scribe circum- 439-443 . 154-159 Equivalent and isoperimetric 436 . Radius and apothem de- 444-446 . triangles The circle ...
... inscribed hexagon equals radius PAGE 159 ures . 438 . Isoperimetric defined . 159 427-435 . To inscribe and scribe circum- 439-443 . 154-159 Equivalent and isoperimetric 436 . Radius and apothem de- 444-446 . triangles The circle ...
Página 126
... inscribed in the circle . PROBLEM I 355. Through any three points not in the same line , to de- scribe a circle . GIVEN , three points , A , B , and C , not in the same line . REQUIRED , to describe a circle which shall pass through all ...
... inscribed in the circle . PROBLEM I 355. Through any three points not in the same line , to de- scribe a circle . GIVEN , three points , A , B , and C , not in the same line . REQUIRED , to describe a circle which shall pass through all ...
Página 128
... inscribed angle is formed by two chords from the same point on the circle , and is said to stand upon the arc between its arms . B Hy THEOREM XII . 365. In the same or equal circles 128 THE ELEMENTs of GEOMETRY . Angles at the Center.
... inscribed angle is formed by two chords from the same point on the circle , and is said to stand upon the arc between its arms . B Hy THEOREM XII . 365. In the same or equal circles 128 THE ELEMENTs of GEOMETRY . Angles at the Center.
Página 132
... inscribed angle standing upon the same arc . D я FIG . I. FIG . 2 . HYPOTHESIS . Let AB be any arc , O the center , C any point on the circle not on arc AB . CONCLUSION . AOB = 24 ACB . PROOF . Join CO , and produce it to D. Because ...
... inscribed angle standing upon the same arc . D я FIG . I. FIG . 2 . HYPOTHESIS . Let AB be any arc , O the center , C any point on the circle not on arc AB . CONCLUSION . AOB = 24 ACB . PROOF . Join CO , and produce it to D. Because ...
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Términos y frases comunes
ABCD alternate angles altitude angles are equal angles equal angles opposite base bisect called chord circumcenter coincide common commutative law CONCLUSION construction COROLLARY cross-ratio describe diagonals diameter divided draw equal are congruent equal sects equiangular equivalent exterior angle figure given line given point given sect greater greatest common divisor hypothenuse HYPOTHESIS included angle inscribed inscribed angle intercepted interior intersecting lines isosceles triangle less locus magnitudes meet mid-point multiples number of sides pair parallelogram pass perigon perimeter perpendicular bisector plane MN prismatoid PROOF proportional quadrilateral radii radius ratio rectangle rectangle contained regular polygon respectively equal rhombus right angle Rule of Inversion sect joining segment sides equal sphere spherical polygon square straight angle subtended supplemental surface symmetrical tangent THEOREM THEOREM VIII three sides transversal triangles are congruent vertex
Pasajes populares
Página 44 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Página 112 - 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.
Página 24 - A right-angled triangle is one which has a right angle. The side opposite the right angle is called the hypothenuse.
Página 190 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 101 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Página 266 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.
Página 13 - An Acute Angle is one which is less than a right angle.
Página 104 - 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, together with the square...
Página 107 - In an obtuse-angled triangle the square on the side opposite the obtuse angle is greater than the sum of the squares on the other two sides by twice the rectangle contained by either side and the projection on it of the other side.
Página 103 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.