Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an Appendix, Notes and IllustrationsJames Ballantyne and Company, 1809 - 493 páginas |
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Página 19
... supposed to turn about the point C in the direction of AB , the angle which it makes with the intercepted part of the line from A will continu- ally diminish . 1 Cor . Hence from any point only one straight BOOK I. 19.
... supposed to turn about the point C in the direction of AB , the angle which it makes with the intercepted part of the line from A will continu- ally diminish . 1 Cor . Hence from any point only one straight BOOK I. 19.
Página 56
... intercepted from the base by perpendiculars let fall them from its oppo- site extremities . upon Let the perpendiculars AP , CN be let fall from the points A , C upon the opposite sides BC and AB of the tri- angle ABC ; the square of AC ...
... intercepted from the base by perpendiculars let fall them from its oppo- site extremities . upon Let the perpendiculars AP , CN be let fall from the points A , C upon the opposite sides BC and AB of the tri- angle ABC ; the square of AC ...
Página 71
... intercepted between the ver- tex of that angle and the perpendicular . - In the oblique - angled triangle ABC , where the perpen- dicular BD falls without the base ; the square of the side AB which subtends the oblique angle exceeds the ...
... intercepted between the ver- tex of that angle and the perpendicular . - In the oblique - angled triangle ABC , where the perpen- dicular BD falls without the base ; the square of the side AB which subtends the oblique angle exceeds the ...
Página 95
... intercepted arc AC is equal to BD . For join AD . And because the straight lines AB and CD are paral- lel , the alternate angles BAD and ADC are equal ( I. 25. ) ; wherefore these angles , having their vertices in the circumference of ...
... intercepted arc AC is equal to BD . For join AD . And because the straight lines AB and CD are paral- lel , the alternate angles BAD and ADC are equal ( I. 25. ) ; wherefore these angles , having their vertices in the circumference of ...
Página 96
... intercepted arcs AD and BC . For draw the chord BF parallel to CD ( III . 22. cor . ) Because ED and BF are parallel , the angle AED ( I. 25. ) is equal to the interior angle ABF , which stands on the arc AF ; but since the chords BF ...
... intercepted arcs AD and BC . For draw the chord BF parallel to CD ( III . 22. cor . ) Because ED and BF are parallel , the angle AED ( I. 25. ) is equal to the interior angle ABF , which stands on the arc AF ; but since the chords BF ...
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Términos y frases comunes
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
Pasajes populares
Página 460 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Página 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.
Página 145 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Página 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.
Página 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.
Página 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...
Página 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.
Página 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.
Página 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...
Página 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.