Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an Appendix, Notes and IllustrationsJames Ballantyne and Company, 1809 - 493 sider |
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Resultat 1-5 av 55
Side 14
... double of ABC , ABE triple , ABF quadruple , ABG quin- tuple , & c . If the sides AB and BC of the given an- gle be supposed equal , only one circle will be required , a series of equal isosceles tri- angles being constituted about its ...
... double of ABC , ABE triple , ABF quadruple , ABG quin- tuple , & c . If the sides AB and BC of the given an- gle be supposed equal , only one circle will be required , a series of equal isosceles tri- angles being constituted about its ...
Side 34
... double of those of an- other triangle ; its remaining opposite interior angle will also be double of the corresponding angle of the other . PROP . XXXV . THEOR . The angles round any 11 34 ELEMENTS OF GEOMETRY . PROP. XXXIV. THEOR. ...
... double of those of an- other triangle ; its remaining opposite interior angle will also be double of the corresponding angle of the other . PROP . XXXV . THEOR . The angles round any 11 34 ELEMENTS OF GEOMETRY . PROP. XXXIV. THEOR. ...
Side 47
... doubles , or the triangle ABCD and the rhomboid DEFC are equivalent . PROP . VIII . PROB . To construct a rhomboid equivalent to a given rectilineal figure , and having its angle equal to a given angle . Let it be required to construct ...
... doubles , or the triangle ABCD and the rhomboid DEFC are equivalent . PROP . VIII . PROB . To construct a rhomboid equivalent to a given rectilineal figure , and having its angle equal to a given angle . Let it be required to construct ...
Side 51
... the parallelograms KB and KE are evidently rectangular ; they are also equal , being contained by equal sides ; and each of them being double of the original tri- angle ACB , they are together equal to the four BOOK II . 51.
... the parallelograms KB and KE are evidently rectangular ; they are also equal , being contained by equal sides ; and each of them being double of the original tri- angle ACB , they are together equal to the four BOOK II . 51.
Side 69
... double of DE ( II . 13. cor . ) ; and consequently the difference between the squares of AE and CE , being equivalent to the rectangle contained by AE and the double of CE , is equivalent to twice the rect- angle under AE and CE . DE ...
... double of DE ( II . 13. cor . ) ; and consequently the difference between the squares of AE and CE , being equivalent to the rectangle contained by AE and the double of CE , is equivalent to twice the rect- angle under AE and CE . DE ...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... Sir John Leslie Uten tilgangsbegrensning - 1811 |
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 460 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Side 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.
Side 145 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Side 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.
Side 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.
Side 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...
Side 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.
Side 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.
Side 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...
Side 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.