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 35
... twice as many right angles , abating four from the result , as the figure has sides . For assume any point O within the figure , and draw straight lines OA , OB , OC , OD , and OE , to the several angular points . It is obvious , that ...
... twice as many right angles , abating four from the result , as the figure has sides . For assume any point O within the figure , and draw straight lines OA , OB , OC , OD , and OE , to the several angular points . It is obvious , that ...
Σελίδα 36
... twice as many right angles as the figure has sides . Conse- quently the exterior angles are equal to the four right angles which , by the last Proposition , were abated , to form the ag- gregate of the interior angles . I B D E F Cor ...
... twice as many right angles as the figure has sides . Conse- quently the exterior angles are equal to the four right angles which , by the last Proposition , were abated , to form the ag- gregate of the interior angles . I B D E F Cor ...
Σελίδα 50
... twice AE and twice EF , that is , to twice AF ; consequently AF is half the sum of BC and AD . Where- fore the rectangle contained by the altitude of the trapezoid and half E F the sum of its parallel sides , is equivalent to the ...
... twice AE and twice EF , that is , to twice AF ; consequently AF is half the sum of BC and AD . Where- fore the rectangle contained by the altitude of the trapezoid and half E F the sum of its parallel sides , is equivalent to the ...
Σελίδα 58
... twice their rectangle . If AB and BC be two straight lines placed continuous ; the square described on their sum AC , is equivalent to the two squares of AB , BC , and twice the rectangle contained by them . For through B draw BI ...
... twice their rectangle . If AB and BC be two straight lines placed continuous ; the square described on their sum AC , is equivalent to the two squares of AB , BC , and twice the rectangle contained by them . For through B draw BI ...
Σελίδα 59
... twice the rectangle contained by these lines . PROP . XXII . THEOR . The square described on the difference of two straight lines , is equivalent to the squares of those lines , diminished by twice their rectangle . Let AC be the ...
... twice the rectangle contained by these lines . PROP . XXII . THEOR . The square described on the difference of two straight lines , is equivalent to the squares of those lines , diminished by twice their rectangle . Let AC be the ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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.