Plane and Solid GeometryCentury Company, 1906 - 418 σελίδες |
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Σελίδα ix
... proved , and most references , including the postulates , are quoted in full . The subject - matter is so arranged that no page must be turned in reading a demonstration . - Brevity . While brevity is not made an end in itself , yet ...
... proved , and most references , including the postulates , are quoted in full . The subject - matter is so arranged that no page must be turned in reading a demonstration . - Brevity . While brevity is not made an end in itself , yet ...
Σελίδα 2
... proving that the supposition that it is not true involves an absurdity . 17 A theorem consists of two parts , the ... proved . Thus : Hypothesis : If A is B , Conclusion C is D. 19 The converse of a theorem is the proposition formed by ...
... proving that the supposition that it is not true involves an absurdity . 17 A theorem consists of two parts , the ... proved . Thus : Hypothesis : If A is B , Conclusion C is D. 19 The converse of a theorem is the proposition formed by ...
Σελίδα 14
... hypothesis . Sup .. supplement . quod erat demonstrandum , which was to be proved . Q.E.F .. quod erat faciendum , which was to be done . • PLANE GEOMETRY BOOK I RECTILINEAR FIGURES PROPOSITION I. THEOREM 100 14 GEOMETRY.
... hypothesis . Sup .. supplement . quod erat demonstrandum , which was to be proved . Q.E.F .. quod erat faciendum , which was to be done . • PLANE GEOMETRY BOOK I RECTILINEAR FIGURES PROPOSITION I. THEOREM 100 14 GEOMETRY.
Σελίδα 17
... Proved Ax . 4 § 103 Proved Ax . 4 ab M N 110 COROLLARY . The exterior sides of supplementary adja- cent angles are in the same straight line . For a + b = a st . 2 . .. MN is a st . line . § 109 " A straight angle is an angle whose ...
... Proved Ax . 4 § 103 Proved Ax . 4 ab M N 110 COROLLARY . The exterior sides of supplementary adja- cent angles are in the same straight line . For a + b = a st . 2 . .. MN is a st . line . § 109 " A straight angle is an angle whose ...
Σελίδα 19
... prove a + ≤ b = a rt . Z. What is the sum of the four ? a and b are half this sum by hyp . ] п- * K 4 22 The bisectors of complementary adjacent angles include an angle of 45 ° . [ Follow the line of proof given in Ex . 21 ...
... prove a + ≤ b = a rt . Z. What is the sum of the four ? a and b are half this sum by hyp . ] п- * K 4 22 The bisectors of complementary adjacent angles include an angle of 45 ° . [ Follow the line of proof given in Ex . 21 ...
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Άλλες εκδόσεις - Προβολή όλων
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...