Plane and Solid GeometryMacmillan, 1901 - 370 σελίδες |
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Αποτελέσματα 1 - 5 από τα 45.
Σελίδα 74
... chord B 166. A chord is a straight line joining any two points in the circumference ; as AB . 167. A central angle is an angle formed by two radii ; as A. 168. Circles having the same center are called concentric . PRELIMINARY THEOREMS ...
... chord B 166. A chord is a straight line joining any two points in the circumference ; as AB . 167. A central angle is an angle formed by two radii ; as A. 168. Circles having the same center are called concentric . PRELIMINARY THEOREMS ...
Σελίδα 75
... chord AB and a diameter AC are drawn , a radius parallel to AB bisects arc BC . Ex . 300. If through a point equidistant from two points in the circum- ference a radius is drawn , the arc between the two points is bisected . Ex . 301 ...
... chord AB and a diameter AC are drawn , a radius parallel to AB bisects arc BC . Ex . 300. If through a point equidistant from two points in the circum- ference a radius is drawn , the arc between the two points is bisected . Ex . 301 ...
Σελίδα 76
... chords are equal . 176. DEF . A polygon is inscribed in a circle , if all its ver- tices are in the circumference ... chords ; and , conversely , equal chords subtend equal arcs . B Hyp . In equal , O and O ' , To prove Of arc AB arc A'B ...
... chords are equal . 176. DEF . A polygon is inscribed in a circle , if all its ver- tices are in the circumference ... chords ; and , conversely , equal chords subtend equal arcs . B Hyp . In equal , O and O ' , To prove Of arc AB arc A'B ...
Σελίδα 77
... chord AB = chord A'B ' . CONVERSELY . - Hyp . In equal , O and O ' , To prove AB = A'B ' . arc AB = arc A'B ' . Q.E.D. HINT . - Draw radii OA , OB , O'A ' , O'B ' , and prove the equality of AOAB and O'A'B ' . Ex . 306. If chords AB ...
... chord AB = chord A'B ' . CONVERSELY . - Hyp . In equal , O and O ' , To prove AB = A'B ' . arc AB = arc A'B ' . Q.E.D. HINT . - Draw radii OA , OB , O'A ' , O'B ' , and prove the equality of AOAB and O'A'B ' . Ex . 306. If chords AB ...
Σελίδα 78
... chord and the subtended arc . E B D Hyp . In O 0 , To prove HINT . the radius OD LAB . AE = EB . arc AD arc DB ... chord passes through the center of the circle . Ex . 313. If two chords are equal , the perpendiculars from the center ...
... chord and the subtended arc . E B D Hyp . In O 0 , To prove HINT . the radius OD LAB . AE = EB . arc AD arc DB ... chord passes through the center of the circle . Ex . 313. If two chords are equal , the perpendiculars from the center ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angles are equal base angles bisect bisector chord circumference circumscribed cone cylinder diagonals diagram for Prop diameter diedral angles divide draw drawn equiangular equiangular polygon equilateral triangle equivalent exterior angle face angles find a point Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous hypotenuse inches inscribed intersecting isosceles triangle joining the midpoints lateral area lateral edges line joining mean proportional median opposite sides parallel lines parallelogram parallelopiped perimeter perpendicular plane MN point equidistant polyedral angle polyedron PROPOSITION prove Proof quadrilateral radii ratio rectangle regular polygon respectively equal rhombus right angles right triangle SCHOLIUM segments sphere spherical polygon spherical triangle square straight angle straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal triedral vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 146 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Σελίδα 248 - A straight line perpendicular to one of two parallel planes is perpendicular to the other also.
Σελίδα 165 - The area of a rectangle is equal to the product of its base and altitude. 1\ u Hyp.
Σελίδα 303 - A cylinder is a solid bounded by a cylindrical surface and two parallel planes ; the bases of a cylinder are the parallel planes; and the lateral surface is the cylindrical surface.
Σελίδα 45 - ... the third side of the first is greater than the third side of the second.
Σελίδα 117 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 29 - The median to the base of an isosceles triangle is perpendicular to the base.
Σελίδα 178 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Σελίδα 150 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 148 - If, from a jwint without a circle, a tangent and a secant be drawn, the tangent is the mean proportional between the secant and UK external segment.