Plane and Solid GeometryCentury Company, 1906 - 418 σελίδες |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 2
... hypothesis and the conclusion . 18 The hypothesis sets forth the things given or granted , either in the statement of a theorem or in the course of the demonstration . ~ The conclusion sets forth the things to be proved . Thus : Hypothesis ...
... hypothesis and the conclusion . 18 The hypothesis sets forth the things given or granted , either in the statement of a theorem or in the course of the demonstration . ~ The conclusion sets forth the things to be proved . Thus : Hypothesis ...
Σελίδα 15
... HYPOTHESIS . The ABC and A'B'C ' are any two straight . CONCLUSION . Z ABC = 4 A'B'C ' . PROOF -C ' Place the ABC on the A'B'C ' so that the vertex B falls on the vertex B ' , and the line BA along the line B'A ' . Then BC will fall ...
... HYPOTHESIS . The ABC and A'B'C ' are any two straight . CONCLUSION . Z ABC = 4 A'B'C ' . PROOF -C ' Place the ABC on the A'B'C ' so that the vertex B falls on the vertex B ' , and the line BA along the line B'A ' . Then BC will fall ...
Σελίδα 16
... HYPOTHESIS . The line AD meets the line BC at D. CONCLUSION . ADB + ≤ ADC = 2 rt . Æ . PROOF ZADB + ADC = the st . △ BDC + ≤ Ax . 13 = 2 rt . s . " A st . is equal to two rt . 4. ” § 70 Q. E. D. 104 COROLLARY 1. The complements of ...
... HYPOTHESIS . The line AD meets the line BC at D. CONCLUSION . ADB + ≤ ADC = 2 rt . Æ . PROOF ZADB + ADC = the st . △ BDC + ≤ Ax . 13 = 2 rt . s . " A st . is equal to two rt . 4. ” § 70 Q. E. D. 104 COROLLARY 1. The complements of ...
Σελίδα 19
... HYPOTHESIS . AB and CD are two intersecting lines . CONCLUSION . Z < m < m = ≤ n , and s = Lt. PROOF Zm is the sup . of △ s , and n is the sup . of △ s . § 103 :: < m = < n . · . < m " The supplements of equal Likewise s = L t . are ...
... HYPOTHESIS . AB and CD are two intersecting lines . CONCLUSION . Z < m < m = ≤ n , and s = Lt. PROOF Zm is the sup . of △ s , and n is the sup . of △ s . § 103 :: < m = < n . · . < m " The supplements of equal Likewise s = L t . are ...
Σελίδα 22
... HYPOTHESIS . AB and CD are parallel lines , and GH is perpendicular to AB . CONCLUSION . GH is perpendicular to CD . PROOF Through H draw EF 1 to GH . " A straight line can be drawn from any point in any direction to any extent . " Then ...
... HYPOTHESIS . AB and CD are parallel lines , and GH is perpendicular to AB . CONCLUSION . GH is perpendicular to CD . PROOF Through H draw EF 1 to GH . " A straight line can be drawn from any point in any direction to any extent . " Then ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angles are equal arc BC assigned quantity base bisectors bisects chord circumference circumscribed Compute CONCLUSION cone construct COROLLARY cylinder diagonals diameter diedral angles divided equiangular equiangular polygon equidistant equilateral triangle exterior angle Find the area Find the locus frustum given circle given line given point homologous hypotenuse HYPOTHESIS inches inscribed intersect isosceles trapezoid isosceles triangle lateral area legs lune median mid-points number of sides opposite parallel lines parallelogram parallelopiped perimeter perpendicular polyedral angle polyedron prism PROOF Draw PROOF Let Prove pyramid Q. E. D. EXERCISES Q. E. D. PROPOSITION quadrilateral radii radius ratio rectangle regular polygon rhombus right angles right triangle SCHOLIUM secant segment semicircle spherical angle spherical degrees spherical excess spherical polygon spherical triangle straight line surface symmetrical tangent tetraedron THEOREM trapezoid triangle ABC triedral vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 168 - 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 that side.
Σελίδα 41 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα 38 - ... 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 35 - Any side of a triangle is less than the sum of the other two sides...
Σελίδα 174 - In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector.
Σελίδα 172 - If from a point without a circle a tangent and a secant are drawn, the tangent is the mean proportional between the whole secant and its external segment.
Σελίδα 171 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Σελίδα 199 - Two triangles having 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.
Σελίδα 192 - The areas of two rectangles having equal altitudes are to each other as their bases.
Σελίδα 65 - The perpendicular bisectors of the sides of a triangle meet in a point. 12. The bisectors of the angles of a triangle meet in a point. 13. The tangents to a circle from an external point are equal. 14...