Plane and Solid GeometryCentury Company, 1906 - 418 σελίδες |
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Αποτελέσματα 1 - 5 από τα 41.
Σελίδα 140
... proportional between a and c . 326 A continued proportion is a series of equal ratios ; as , a : b c : de : f = g : h . 327 SCHOLIUM . In Geometry it is assumed that the four quantities of a proportion are represented by their numerical ...
... proportional between a and c . 326 A continued proportion is a series of equal ratios ; as , a : b c : de : f = g : h . 327 SCHOLIUM . In Geometry it is assumed that the four quantities of a proportion are represented by their numerical ...
Σελίδα 141
... proportional between two quantities is equal to the square root of their product . HYPOTHESIS . CONCLUSION . a : bb ... proportional between 3 and 27 . § 328 Q. E. D. 572 Find the mean proportional between m and n . THEORY OF PROPORTION ...
... proportional between two quantities is equal to the square root of their product . HYPOTHESIS . CONCLUSION . a : bb ... proportional between 3 and 27 . § 328 Q. E. D. 572 Find the mean proportional between m and n . THEORY OF PROPORTION ...
Σελίδα 142
... proportional to 2 and 6 . 574 Find the third proportional to m and n . PROPOSITION III . THEOREM 330 If the product of two quantities is equal to the product of two others , either two may be made the extremes and the other two the ...
... proportional to 2 and 6 . 574 Find the third proportional to m and n . PROPOSITION III . THEOREM 330 If the product of two quantities is equal to the product of two others , either two may be made the extremes and the other two the ...
Σελίδα 148
... proportionally . A E E D B ' m B C B Fig . 1 Fig . 2 HYPOTHESIS . In the triangle ABC , DE is parallel to BC . CONCLUSION . BD : DA = CE : EA . CASE 1. When BD and DA are commensurable ( Fig . 1 ) . PROOF Let m , a common measure of BD ...
... proportionally . A E E D B ' m B C B Fig . 1 Fig . 2 HYPOTHESIS . In the triangle ABC , DE is parallel to BC . CONCLUSION . BD : DA = CE : EA . CASE 1. When BD and DA are commensurable ( Fig . 1 ) . PROOF Let m , a common measure of BD ...
Σελίδα 149
... proportional . E D For AD : AE and AD : AE = = BD : CE , DF : EG . F Also , AF : AG = DF : EG , and AF : AG .. BD : CE = DF : EG = FH : GK . = FH : GK . H K PROPOSITION XIV . THEOREM 343 If a straight line divides THEORY OF PROPORTION 149.
... proportional . E D For AD : AE and AD : AE = = BD : CE , DF : EG . F Also , AF : AG = DF : EG , and AF : AG .. BD : CE = DF : EG = FH : GK . = FH : GK . H K PROPOSITION XIV . THEOREM 343 If a straight line divides THEORY OF PROPORTION 149.
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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...