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 11
... equal , AC is equal to G ; and for the same reason , BC is equal to H. Con- H sequently the triangle ACB answers the conditions of the problem . Corollary . If the radii G and H be equal to each other , the triangle will evidently be ...
... equal , AC is equal to G ; and for the same reason , BC is equal to H. Con- H sequently the triangle ACB answers the conditions of the problem . Corollary . If the radii G and H be equal to each other , the triangle will evidently be ...
Σελίδα 12
... equal to EDF , ACB to DEF , and CBA to EFD ; the equal angles being thus al- ways opposite to the equal sides . PROP . III . THEOR . Two triangles are equal , if two sides and the an- gle contained by these in the one be respectively equal ...
... equal to EDF , ACB to DEF , and CBA to EFD ; the equal angles being thus al- ways opposite to the equal sides . PROP . III . THEOR . Two triangles are equal , if two sides and the an- gle contained by these in the one be respectively equal ...
Σελίδα 13
... equal , and the angles BAC , BCA opposite to BC and BA are equal respectively to EDF and EFD , which the corre- sponding sides EF and ED subtend . PROP . IV . PROB . At a point in a straight line , to make an angle equal to a given ...
... equal , and the angles BAC , BCA opposite to BC and BA are equal respectively to EDF and EFD , which the corre- sponding sides EF and ED subtend . PROP . IV . PROB . At a point in a straight line , to make an angle equal to a given ...
Σελίδα 14
... equal to the original triangle ABC . Consequently the angle ABD is 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 ...
... equal to the original triangle ABC . Consequently the angle ABD is 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 ...
Σελίδα 15
... equal to DF , CE to FE , and DE common to them both ; whence ( I. 2. ) the angle CDE or CDG is equal to FDE or FDG . And because in the triangles DCG and DFG , the side DC is equal to DF , DG is com- mon , and the contained angles CDG ...
... equal to DF , CE to FE , and DE common to them both ; whence ( I. 2. ) the angle CDE or CDG is equal to FDE or FDG . And because in the triangles DCG and DFG , the side DC is equal to DF , DG is com- mon , and the contained angles CDG ...
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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.