Essentials of GeometryS.C. Griggs, 1883 - 267 σελίδες |
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Σελίδα viii
... theorems of which original demonstration is required , are appended , with liberal suggestions , to many sections and at the end of every chapter ; of sufficient dif- ficulty to stimulate to success , yet not so ... theorem viii PREFACE .
... theorems of which original demonstration is required , are appended , with liberal suggestions , to many sections and at the end of every chapter ; of sufficient dif- ficulty to stimulate to success , yet not so ... theorem viii PREFACE .
Σελίδα ix
... theorem is stated in connection with its converse . Separate topics are made separate lessons . Notation has been greatly reduced . Where it has been customary to use many letters in designating the diagram , I have , where possible ...
... theorem is stated in connection with its converse . Separate topics are made separate lessons . Notation has been greatly reduced . Where it has been customary to use many letters in designating the diagram , I have , where possible ...
Σελίδα 15
... theorem , that which is given or assumed , in order to 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 ...
... theorem , that which is given or assumed , in order to 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 ...
Σελίδα 17
... THEOREM V. 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 triangles will be equal in all their parts . Let ABC and DEF be two tri- A D angles ...
... THEOREM V. 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 triangles will be equal in all their parts . Let ABC and DEF be two tri- A D angles ...
Σελίδα 18
... Theorem is Conclusion ? 2. What part of Theorem I is Hypothesis ? Of Theorem II ? 3. What part of each is Conclusion ? 4. Which is the precise thing to be proved , the Hypothesis or the Con- clusion ? 5. In Theorem VI , what is given ...
... Theorem is Conclusion ? 2. What part of Theorem I is Hypothesis ? Of Theorem II ? 3. What part of each is Conclusion ? 4. Which is the precise thing to be proved , the Hypothesis or the Con- clusion ? 5. In Theorem VI , what is given ...
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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.