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
... common to them both , being placed in the middle . Thus the angle contained by the straight lines AB and BC , or the opening formed by the revolution of BA about the point B into the position BC , is named ABC or CBA . 4. A right angle ...
... common to them both , being placed in the middle . Thus the angle contained by the straight lines AB and BC , or the opening formed by the revolution of BA about the point B into the position BC , is named ABC or CBA . 4. A right angle ...
Σελίδα 7
... common angle ABD , there remains CBA equal to DBE . 11. Two straight lines are said to be inclined to each other , if they meet when produced ; and the angle so for- med is called their inclination . 12. Straight lines which have no ...
... common angle ABD , there remains CBA equal to DBE . 11. Two straight lines are said to be inclined to each other , if they meet when produced ; and the angle so for- med is called their inclination . 12. Straight lines which have no ...
Σελίδα 12
... common to both those circles , or in F the vertex of the triangle DFE . Conse- quently those two triangles , being rectilineal , must entire- ly coincide . The angle CAB is equal to EDF , ACB to DEF , and CBA to EFD ; the equal angles ...
... common to both those circles , or in F the vertex of the triangle DFE . Conse- quently those two triangles , being rectilineal , must entire- ly coincide . The angle CAB is equal to EDF , ACB to DEF , and CBA to EFD ; the equal angles ...
Σελίδα 15
... 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 and FDG are proved to be equal ...
... 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 and FDG are proved to be equal ...
Σελίδα 16
... common to them both ; these triangles ( I. 2. ) are equal , and the angle ACD or ACE is equal to BCD or BCE . Again , the triangles ACE and BCE , having the side AC equal to BC , CE common , and the contained angle ACE equal to BCE ...
... common to them both ; these triangles ( I. 2. ) are equal , and the angle ACD or ACE is equal to BCD or BCE . Again , the triangles ACE and BCE , having the side AC equal to BC , CE common , and the contained angle ACE equal to BCE ...
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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.