Plane and Solid GeometryCentury Company, 1906 - 418 σελίδες |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 2
... 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 : If A is B , ...
... 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 : If A is B , ...
Σελίδα 16
... CONCLUSION . ADB + ≤ ADC = 2 rt . . 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 equal angles are equal . 105 COROLLARY 2. The supplements of ...
... CONCLUSION . ADB + ≤ ADC = 2 rt . . 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 equal angles are equal . 105 COROLLARY 2. The supplements of ...
Σελίδα 19
... CONCLUSION . ≤ m = ≤ n , and ≤ s = Lt. PROOF Zm is the sup . of ≤ s , and n is the sup . of s . :: < m = Ln . § 103 " The supplements of equal are equal . " § 105 Q. E. D. Likewise s = Lt. EXERCISES 17 If ≤1 = 38 ° , find ≤3 , 24 ...
... CONCLUSION . ≤ m = ≤ n , and ≤ s = Lt. PROOF Zm is the sup . of ≤ s , and n is the sup . of s . :: < m = Ln . § 103 " The supplements of equal are equal . " § 105 Q. E. D. Likewise s = Lt. EXERCISES 17 If ≤1 = 38 ° , find ≤3 , 24 ...
Σελίδα 21
... CONCLUSION . a and b are parallel . PROOF Could a and b , upon being produced , meet at some point , as at X , there would be two perpendiculars drawn from the point X to the line m , which is impossible . “ From a point without a line ...
... CONCLUSION . a and b are parallel . PROOF Could a and b , upon being produced , meet at some point , as at X , there would be two perpendiculars drawn from the point X to the line m , which is impossible . “ From a point without a line ...
Σελίδα 36
... CONCLUSION . △ ABC = A DEF . PROOF Place the △ ABC on the △ DEF so that the equal A and D shall coincide , AB falling along DE , and AC along DF . Then B will fall on E , for AB = DE by hypothesis ; and C will fall on F , for AC DF ...
... CONCLUSION . △ ABC = A DEF . PROOF Place the △ ABC on the △ DEF so that the equal A and D shall coincide , AB falling along DE , and AC along DF . Then B will fall on E , for AB = DE by hypothesis ; and C will fall on F , for AC DF ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angles are equal arc BC assigned quantity base bisectors bisects chord circumference circumscribed circle CONCLUSION cone construct COROLLARY cylinder diagonals diameter diedral angles divided equiangular equiangular polygon equidistant equilateral triangle exterior angle Find the area Find the locus Find the ratio frustum given circle given line given point homologous sides hypotenuse HYPOTHESIS inches inscribed intersecting isosceles trapezoid isosceles triangle lateral area legs line of centers mean proportional median mid-points number of sides parallelogram parallelopiped perimeter perpendicular polyedral angle polyedron prism PROOF Draw Prove pyramid Q. E. D. EXERCISES Q. E. D. PROPOSITION quadrilateral radii radius rectangle regular polygon rhombus right angles right triangle SCHOLIUM secant segments similar triangles slant height SOLUTION sphere spherical polygon spherical triangle straight line surface tangent THEOREM trapezoid triangle ABC triedral vertex volume
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 242 - The areas of two triangles which have 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
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 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...