Essentials of GeometryS.C. Griggs, 1883 - 267 σελίδες |
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Σελίδα v
... V. CONSTRUCTIONS , 81 CHAPTER VI . EQUALITY AND MEASUREMENT OF POLYGONS , 101 CHAPTER VII . PROPORTIONALITY OF LINES , . 121 CHAPTER VIII . SIMILARITY OF POLYGONS , 126 CHAPTER IX . CONSTRUCTIONS , 142 CHAPTER X. REGULAR POLYGONS V.
... V. CONSTRUCTIONS , 81 CHAPTER VI . EQUALITY AND MEASUREMENT OF POLYGONS , 101 CHAPTER VII . PROPORTIONALITY OF LINES , . 121 CHAPTER VIII . SIMILARITY OF POLYGONS , 126 CHAPTER IX . CONSTRUCTIONS , 142 CHAPTER X. REGULAR POLYGONS V.
Σελίδα 14
... measured straight line A C , is less than the distance between the same points measured on the broken line A B C Ax . 8 . Hence , Likewise , and ( 1 ) A CAB + B C. ( 2 ) A BACA B. ( 3 ) BC A C + A B. Second : Any side will be greater ...
... measured straight line A C , is less than the distance between the same points measured on the broken line A B C Ax . 8 . Hence , Likewise , and ( 1 ) A CAB + B C. ( 2 ) A BACA B. ( 3 ) BC A C + A B. Second : Any side will be greater ...
Σελίδα 71
... Measure . Thus , to measure a line is to find how many times it contains another line called the unit of length , or linear unit . 2. The number expressing how many times a quantity con- tains its unit , is called the numerical measure ...
... Measure . Thus , to measure a line is to find how many times it contains another line called the unit of length , or linear unit . 2. The number expressing how many times a quantity con- tains its unit , is called the numerical measure ...
Σελίδα 72
Alfred Hix Welsh. 4. Two quantities are commensurable when they have a common measure . 5. Two quantities are incommensurable when they have no common measure ; that is , when no assumed unit is contained in each without a remainder ...
Alfred Hix Welsh. 4. Two quantities are commensurable when they have a common measure . 5. Two quantities are incommensurable when they have no common measure ; that is , when no assumed unit is contained in each without a remainder ...
Σελίδα 74
... measure , to be contained in ACB 7 times , and in E D F 4 times ; then ( 1 ) A CB : EDF :: 7 : 4 . Since the partial angles are equal , being each equal to m , they intercept equal arcs ( Th . XVII ) ; hence A B is divided into 7 equal ...
... measure , to be contained in ACB 7 times , and in E D F 4 times ; then ( 1 ) A CB : EDF :: 7 : 4 . Since the partial angles are equal , being each equal to m , they intercept equal arcs ( Th . XVII ) ; hence A B is divided into 7 equal ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 18 - if two triangles have two sides of the one equal to two sides of the...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 38 - If two sides of a quadrilateral are equal and parallel, the figure is a parallelogram.
Σελίδα 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.
Σελίδα 232 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Σελίδα 14 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα 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.