Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an Appendix, Notes and IllustrationsJames Ballantyne and Company, 1809 - 493 σελίδες |
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Σελίδα 150
... mean proportional between the two extremes . 18. The ratio which one quantity has to another may be considered as ... mean ratio , when the one segment is a mean proportional between the other segment and the whole line . To facilitate ...
... mean proportional between the two extremes . 18. The ratio which one quantity has to another may be considered as ... mean ratio , when the one segment is a mean proportional between the other segment and the whole line . To facilitate ...
Σελίδα 156
... means ; and of two equal products , the factors are convertible into an analogy , of which these form severally the ex- treme and the mean terms . Let A : B :: C : D ; then AD = BC . For , if Ama , and C - mc , their consequents , B and ...
... means ; and of two equal products , the factors are convertible into an analogy , of which these form severally the ex- treme and the mean terms . Let A : B :: C : D ; then AD = BC . For , if Ama , and C - mc , their consequents , B and ...
Σελίδα 157
... means . Cor . 2. Hence also a proportion is not affected , by trans- posing or interchanging its extreme and mean terms . On this principle , is founded the two following theorems . PROP . VII . THEOR . The terms of an analogy are ...
... means . Cor . 2. Hence also a proportion is not affected , by trans- posing or interchanging its extreme and mean terms . On this principle , is founded the two following theorems . PROP . VII . THEOR . The terms of an analogy are ...
Σελίδα 161
... mean term of three proportionals , is less than half the sum of both extremes . PROP . XV . THEOR . If two analogies have the same antecedents , ano- ther analogy may be formed , having the consequents of the one as antecedents , and ...
... mean term of three proportionals , is less than half the sum of both extremes . PROP . XV . THEOR . If two analogies have the same antecedents , ano- ther analogy may be formed , having the consequents of the one as antecedents , and ...
Σελίδα 162
... means , the ex- tremes of the one , with those of the other as mean terms , will form a third analogy . 1 . Let A : B :: C : D , and E : B :: C : F ; then A : E :: F : D. For , since A : B :: C : D , AD = BC ( V. 6. ) ; and because E ...
... means , the ex- tremes of the one , with those of the other as mean terms , will form a third analogy . 1 . Let A : B :: C : D , and E : B :: C : F ; then A : E :: F : D. For , since A : B :: C : D , AD = BC ( V. 6. ) ; and because E ...
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ABCD ANALYSIS angle ABC angle ACB angle BAC bisect centre chord circumference COMPOSITION conse consequently the angle decagon describe a circle diameter distance diverging lines draw drawn equal to BC evidently exterior angle fall the perpendicular given circle given in position given point given ratio given space given straight line greater hence hypotenuse inflected inscribed intercepted intersection isosceles triangle join let fall likewise mean proportional parallel perpendicular point F polygon porism PROB PROP quently radius rectangle rectangle contained regular polygon rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter sequently side AC similar sine square of AC squares of AB tangent THEOR triangle ABC twice the square vertex vertical angle whence wherefore
Δημοφιλή αποσπάσματα
Σελίδα 460 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Σελίδα 28 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Σελίδα 145 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Σελίδα 34 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 153 - Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth.
Σελίδα 16 - PROP. V. THEOR. The angles at the base of an isosceles triangle are equal to one another; and if the equal sides be produced, the angles -upon the other side of the base shall be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC, be produced to D and E: the angle ABC shall be equal to the angle ACB, and the angle...
Σελίδα 411 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Σελίδα 58 - Prove, geometrically, that the rectangle of the sum and the difference of two straight lines is equivalent to the difference of the squares of those lines.
Σελίδα 64 - IF a straight line be bisected, and produced to any point: the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Σελίδα 157 - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.