The Elements of GeometryLeach, Shewell & Sanborn, 1894 - 378 σελίδες |
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Σελίδα vii
... radii of a circle are equal . While in general the complete statement of the reference should be insisted on , if the proposition referred to states more than one truth , that portion only need be quoted which applies to the case under ...
... radii of a circle are equal . While in general the complete statement of the reference should be insisted on , if the proposition referred to states more than one truth , that portion only need be quoted which applies to the case under ...
Σελίδα x
... draw OA and OC . Then E is the middle point of AB , and F of CD . [ The diameter 1 to a chord bisects it . ] Now in the rt . A OAE and OCF , AE = CF , being halves of equal chords . Also , OA = = OC . [ All radii X INTRODUCTION .
... draw OA and OC . Then E is the middle point of AB , and F of CD . [ The diameter 1 to a chord bisects it . ] Now in the rt . A OAE and OCF , AE = CF , being halves of equal chords . Also , OA = = OC . [ All radii X INTRODUCTION .
Σελίδα xi
Webster Wells. Also , OA = = OC . [ All radii of a O are equal . ] .. ΔΟΑΕ AOCF . [ Two rt . A are equal when the hypotenuse and a leg of one are equal respectively to the hypotenuse and a leg of the other . ] .. OE OF . [ In equal ...
Webster Wells. Also , OA = = OC . [ All radii of a O are equal . ] .. ΔΟΑΕ AOCF . [ Two rt . A are equal when the hypotenuse and a leg of one are equal respectively to the hypotenuse and a leg of the other . ] .. OE OF . [ In equal ...
Σελίδα 70
... radii . 144. Two circles are equal when their radii are equal . For they can evidently be applied one to the other so that their circumferences shall coincide throughout . 145. Conversely , the radii of equal circles are equal . 146. A ...
... radii . 144. Two circles are equal when their radii are equal . For they can evidently be applied one to the other so that their circumferences shall coincide throughout . 145. Conversely , the radii of equal circles are equal . 146. A ...
Σελίδα 71
... radii drawn to its extremities ; as OCD . 148. A central angle is an angle whose vertex is at the centre , and whose sides are radii ; as AOC . An inscribed angle is an angle whose ver- tex is on the circumference , and whose sides are ...
... radii drawn to its extremities ; as OCD . 148. A central angle is an angle whose vertex is at the centre , and whose sides are radii ; as AOC . An inscribed angle is an angle whose ver- tex is on the circumference , and whose sides are ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles altitude angles are equal approach the limit arc BC area ABC base and altitude BC² bisector bisects centre chord circle circumference circumscribed cone of revolution construct the triangle Converse of Prop cylinder diagonals diameter diedral Draw BC equal respectively equally distant equilateral triangle equivalent exterior angle Find the area frustum given point given straight line Hence homologous hypotenuse intersection isosceles triangle lateral area lateral edges Let ABC measured by arc middle point number of sides O-ABC parallelogram parallelopiped perimeter perpendicular to MN plane MN polyedral polyedron prism produced PROPOSITION prove pyramid quadrilateral radii radius rectangle regular polygon rhombus right angles right triangle secant line segment similar slant height sphere spherical polygon spherical triangle square surface tangent tetraedron THEOREM trapezoid triangle ABC triangles are equal triangular prism triedral vertex volume Whence
Δημοφιλή αποσπάσματα
Σελίδα 165 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 39 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Σελίδα 65 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Σελίδα 172 - 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. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.
Σελίδα 122 - In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Σελίδα 355 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Σελίδα 52 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.
Σελίδα 140 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Σελίδα 123 - In any proportion the terms are in proportion by composition and division ; that is, the sum of the first two terms is to their difference as the sum of the last two terms to their difference.
Σελίδα 207 - S' denote the areas of two © whose radii are R and R', and diameters D and D', respectively. Then, | = "* § = ££ = £• <§337> That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters.