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 7
... exterior angle , and the angle made up of ABD , DBE , and EBC , or the opening formed by the regression of AB through the points D and E into the position BC , is the reverse angle . It is apparent that vertical angles , or those formed ...
... exterior angle , and the angle made up of ABD , DBE , and EBC , or the opening formed by the regression of AB through the points D and E into the position BC , is the reverse angle . It is apparent that vertical angles , or those formed ...
Σελίδα 17
... triangle is also equilateral . PROP . X. THEOR . The exterior angle of a triangle is greater than either of the interior opposite angles . The exterior angle BCF , formed by producing a side AC of the triangle ABC , is greater than ...
... triangle is also equilateral . PROP . X. THEOR . The exterior angle of a triangle is greater than either of the interior opposite angles . The exterior angle BCF , formed by producing a side AC of the triangle ABC , is greater than ...
Σελίδα 18
... angle DCE is equal to DBA . But the angle BCF is evidently greater than DCE , it is con- sequently greater than DBA or ABC . In like manner , it may be shown , that if BC be produced , the exterior angle ACG is greater than CAB . But ...
... angle DCE is equal to DBA . But the angle BCF is evidently greater than DCE , it is con- sequently greater than DBA or ABC . In like manner , it may be shown , that if BC be produced , the exterior angle ACG is greater than CAB . But ...
Σελίδα 19
... angle ACB . The angles ACB and CAB , being less than two right an- gles , and ACB being greater than one B right ... exterior angle of the triangle DCE , and is con- sequently ( I. 10. ) greater than the opposite interior angle CED . ADE ...
... angle ACB . The angles ACB and CAB , being less than two right an- gles , and ACB being greater than one B right ... exterior angle of the triangle DCE , and is con- sequently ( I. 10. ) greater than the opposite interior angle CED . ADE ...
Σελίδα 20
... angle on the same side with a given straight line ; and hence also no more than one per- pendicular can be let fall ... exterior angle of the triangle CAD , is ( I. 10. ) greater than ACD or ACB ; wherefore the angle CAB is much greater ...
... angle on the same side with a given straight line ; and hence also no more than one per- pendicular can be let fall ... exterior angle of the triangle CAD , is ( I. 10. ) greater than ACD or ACB ; wherefore the angle CAB is much greater ...
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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.