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 5
... remaining the same ; CB will , in this new position EB , make an- gles EBA and EBD equal to the former , and therefore all of them equal to each other . But the four angles ABC , CBD , DBE and EBA constitute about the point D a complete ...
... remaining the same ; CB will , in this new position EB , make an- gles EBA and EBD equal to the former , and therefore all of them equal to each other . But the four angles ABC , CBD , DBE and EBA constitute about the point D a complete ...
Σελίδα 19
... remaining angles , such as BAC , be likewise acute , the two angles ACB and BAC are both of them acute . But if the angle BAC be either obtuse or a right an- gle , it comes under the two former cases , and the other angles ABC and ACB ...
... remaining angles , such as BAC , be likewise acute , the two angles ACB and BAC are both of them acute . But if the angle BAC be either obtuse or a right an- gle , it comes under the two former cases , and the other angles ABC and ACB ...
Σελίδα 32
... remaining angles at B and D , being equal to each other and to two right angles , must be right angled . PROP . XXX . THEOR . If the parallel sides of a trapezoid be equal , the other sides are likewise equal and parallel . Let the ...
... remaining angles at B and D , being equal to each other and to two right angles , must be right angled . PROP . XXX . THEOR . If the parallel sides of a trapezoid be equal , the other sides are likewise equal and parallel . Let the ...
Σελίδα 34
... angles , 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 .
... angles , 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 .
Σελίδα 63
... remaining angle BFC is also half a right angle ( I. $ 4 . ) and , therefore , equal to the angle BCF ; whence ( I 9. ) the side BF is equal to BC . By the same reasoning it may be shown , that the right - angled tri- E F A DB C angle ...
... remaining angle BFC is also half a right angle ( I. $ 4 . ) and , therefore , equal to the angle BCF ; whence ( I 9. ) the side BF is equal to BC . By the same reasoning it may be shown , that the right - angled tri- E F A DB C angle ...
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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 drawn equal to BC exterior angle fall the perpendicular given angle 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 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 AB square of AC tangent THEOR triangle ABC twice the square vertex vertical angle whence wherefore
Δημοφιλή αποσπάσματα
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 147 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Σελίδα 92 - THE angle at the centre of a circle is double of the angle at the circumference, upon the same base, that is, upon the same
Σελίδα 458 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Σελίδα 99 - ... a circle. The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle. The opposite angles of any quadrilateral inscribed in a circle are supplementary; and the converse.
Σελίδα 155 - 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 408 - 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 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 36 - 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 60 - 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.