Essentials of GeometryS.C. Griggs, 1883 - 267 sider |
Inni boken
Resultat 1-5 av 17
Side 15
... lateral ? 6. Can two polygons , neither of which is equiangular , be mutually equi- angular . ? METHOD OF SUPERPOSITION . Two geometrical magnitudes are equal in all their parts when they can be so adjusted , one to the other , as to ...
... lateral ? 6. Can two polygons , neither of which is equiangular , be mutually equi- angular . ? METHOD OF SUPERPOSITION . Two geometrical magnitudes are equal in all their parts when they can be so adjusted , one to the other , as to ...
Side 92
... lateral triangle . Angle CAB = 60 ° ; hence , EAC 30 ° . Now , bisect C A B ( Prob . VI ) . Otherwise , on A E construct an equilateral triangle ; then E A D = 60 ° ; ... DAB 30 ° ; but , also , = EA C = 30 ° ; .. CAD = 30 ° . .. = EAC ...
... lateral triangle . Angle CAB = 60 ° ; hence , EAC 30 ° . Now , bisect C A B ( Prob . VI ) . Otherwise , on A E construct an equilateral triangle ; then E A D = 60 ° ; ... DAB 30 ° ; but , also , = EA C = 30 ° ; .. CAD = 30 ° . .. = EAC ...
Side 104
... lateral ? THEOREM II . Rectangles having equal altitudes are proportional to their bases . There may be two cases : the bases may be commensurable , or they may be incommensurable . R b will R R ' :: b : b ' . R First : Let R and R ' be ...
... lateral ? THEOREM II . Rectangles having equal altitudes are proportional to their bases . There may be two cases : the bases may be commensurable , or they may be incommensurable . R b will R R ' :: b : b ' . R First : Let R and R ' be ...
Side 162
... lateral triangle , the square , and the regular hexagon . To cover a surface entirely with a mosaic work of equal poly- gons , they must be such that their angles , when placed with their vertices coincident , will exactly fill the ...
... lateral triangle , the square , and the regular hexagon . To cover a surface entirely with a mosaic work of equal poly- gons , they must be such that their angles , when placed with their vertices coincident , will exactly fill the ...
Side 163
... lateral force , a combination of equilateral triangles or a combination of regular hexagons ? Does the conjunction of angles at the same point weaken the surface and increase the liability to frac- ture ? 2. Why do masons adopt the ...
... lateral force , a combination of equilateral triangles or a combination of regular hexagons ? Does the conjunction of angles at the same point weaken the surface and increase the liability to frac- ture ? 2. Why do masons adopt the ...
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A B and C D ABCD adjacent angles angle equal apothem bisect central angles centre circle whose radius circumference coincide construct convex surface cylinder diagonals diameter distance divided draw drawn equal altitudes equal bases equal circles equally distant equiangular EXERCISES feet frustum generatrix given angle given circle given line given point greater Hence homologous sides hypotenuse included angle inscribed angle inscribed circle interior angles intersect isosceles triangle lune number of sides oblique parallel parallelogram parallelopiped perimeter perpendicular plane prism Prob proportional pyramid Q. E. D. Cor Q. E. F quadrilateral QUERIES radii ratio rectangle regular polygon right cone right triangle Scholium secant segments similar slant height sphere spherical triangle square straight line tangent triangle A B C vertex vertices
Populære avsnitt
Side 18 - if two triangles have two sides of the one equal to two sides of the...
Side 110 - 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 it.
Side 13 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
Side 107 - If two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other, each to each, they are equal in all their parts.
Side 24 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 38 - If two sides of a quadrilateral are equal and parallel, the figure is a parallelogram.
Side 42 - If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let bc=ad.
Side 232 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Side 14 - In an isosceles triangle the angles opposite the equal sides are equal.
Side x - AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will be unequal.