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 3
... meets the third point . The separation or opening of two straight lines at their point of intersection , constitutes an angle . If we obtain the idea of distance , or linear extent , from progressive motion , we derive that of diver ...
... meets the third point . The separation or opening of two straight lines at their point of intersection , constitutes an angle . If we obtain the idea of distance , or linear extent , from progressive motion , we derive that of diver ...
Σελίδα 7
... meet when produced ; and the angle so for- med is called their inclination . 21 12. Straight lines which have no incli- nation are termed parallel . 13. A figure is a plane surface included by a linear boundary called its perimeter . 14 ...
... meet when produced ; and the angle so for- med is called their inclination . 21 12. Straight lines which have no incli- nation are termed parallel . 13. A figure is a plane surface included by a linear boundary called its perimeter . 14 ...
Σελίδα 19
... meet it ; the nearer one will form on the same side a greater angle than that which is more remote . If straight lines CD , CE be drawn from the point C to the straight line AB ; the angle ADC is greater than AEC . For ADC is the ...
... meet it ; the nearer one will form on the same side a greater angle than that which is more remote . If straight lines CD , CE be drawn from the point C to the straight line AB ; the angle ADC is greater than AEC . For ADC is the ...
Σελίδα 23
... meet CB in E. The two sides AB and BE of the triangle ABE are greater than the third side AE ( I. 16. ) ; add EC to each , and AB , BE , EC , or AB and BC , are greater than AE and EC . But the sides CE and ED of the triangle DEC are ...
... meet CB in E. The two sides AB and BE of the triangle ABE are greater than the third side AE ( I. 16. ) ; add EC to each , and AB , BE , EC , or AB and BC , are greater than AE and EC . But the sides CE and ED of the triangle DEC are ...
Σελίδα 24
... meet BC in I. C Because HI is greater than HG , it is greater than the equal side BC , and therefore much greater than BI . Con- sequently the opposite angle IBH of the triangle BIH is ( I. 14. ) greater than BHI . But AB being equal to ...
... meet BC in I. C Because HI is greater than HG , it is greater than the equal side BC , and therefore much greater than BI . Con- sequently the opposite angle IBH of the triangle BIH is ( I. 14. ) greater than BHI . But AB being equal to ...
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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 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
Δημοφιλή αποσπάσματα
Σελίδα 460 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
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 145 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Σελίδα 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.
Σελίδα 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.
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 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.