Essentials of GeometryS.C. Griggs, 1883 - 267 sider |
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Resultat 1-5 av 44
Side 6
... proved . 4. A Corollary is a truth which follows , as a necessary con- sequence , from one or more preceding propositions . 5. A Hypothesis is a supposition assumed to be true in order to argue from it the truth or falsity of a ...
... proved . 4. A Corollary is a truth which follows , as a necessary con- sequence , from one or more preceding propositions . 5. A Hypothesis is a supposition assumed to be true in order to argue from it the truth or falsity of a ...
Side 9
Alfred Hix Welsh. ( 2 ) ACD + DCB 2 R , as just proved ; = .. ( 3 ) a + b + c + d + e + f = 2 R. QUERIES . 1. On what two axioms is ( 1 ) founded ? 2. By what axiom is ( 3 ) deduced from ( 1 ) and ( 2 ) ? What is the thing ' ? What are ...
Alfred Hix Welsh. ( 2 ) ACD + DCB 2 R , as just proved ; = .. ( 3 ) a + b + c + d + e + f = 2 R. QUERIES . 1. On what two axioms is ( 1 ) founded ? 2. By what axiom is ( 3 ) deduced from ( 1 ) and ( 2 ) ? What is the thing ' ? What are ...
Side 11
... Prove , from the annexed diagram , that the straight line which bisects an angle bisects its vertical angle . Suggestion . - Suppose angle A O D to be bisected . the EXERCISES . E 4. Prove , from the annexed diagram , that the bisectors ...
... Prove , from the annexed diagram , that the straight line which bisects an angle bisects its vertical angle . Suggestion . - Suppose angle A O D to be bisected . the EXERCISES . E 4. Prove , from the annexed diagram , that the bisectors ...
Side 15
... prove something else , is the Hypothesis , though the conditional if ' may not be expressed . Thus in the preceding Theorem , the Hypothesis is the given triangle ; that is , if we have a triangle , or if a figure is a triangle . The ...
... prove something else , is the Hypothesis , though the conditional if ' may not be expressed . Thus in the preceding Theorem , the Hypothesis is the given triangle ; that is , if we have a triangle , or if a figure is a triangle . The ...
Side 18
... proved , the Hypothesis or the Con- clusion ? 5. In Theorem VI , what is given , and what is required to be proved ? EXERCISES . 1. State the fact that ' Socrates was mortal , ' in the form of a theorem , with hypothesis and conclusion ...
... proved , the Hypothesis or the Con- clusion ? 5. In Theorem VI , what is given , and what is required to be proved ? EXERCISES . 1. State the fact that ' Socrates was mortal , ' in the form of a theorem , with hypothesis and conclusion ...
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Vanlige uttrykk og setninger
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.