 | Henry Wilson - 1761 - 580 σελίδες
...• i AXIOM IV. In all Triangles, as the Bafe or greater Side, to the Sum of the other two Sides ; fo the Difference of the Sides to the Difference of the Segments of the Bafe, which Difference fubtraered from the whole Bafe, the Perpendicular falls in the Middle of the... | |
 | John Hamilton Moore - 1791 - 578 σελίδες
...AXIOM IVT In any Plane Triangle, as the Bafe or greateft Side is to the Sum pf the other two Sides, fo is the Difference of the Sides to the Difference of the Segments of the Bafe, made by a Perpendicular let fall from the Angle oppofite to the Bafe. ' And if hair the Difference... | |
 | Thomas Simpson - 1810 - 168 σελίδες
...to the sine of its opposite angle. • THEOREM IV. As the base of any plane triangle ABC (fig. 4.) is to the sum of the two sides, so is the difference of the sides to twicf the distance DE of the perpendicular from the middle oftlie base. From the vertex C, with the... | |
 | John Ryley, John Gawthorp, John Whitley - 1815 - 308 σελίδες
...difference of the sides is to the differenc6 of the segments of the base; therefore, as the ratio of the difference of the sides to the difference of the segments of the base, is given, that of the base to the sum, of the sides is given also; but the base is given, consequently,... | |
 | John Playfair - 1819 - 354 σελίδες
...the sides, and therefore (16. 6.) the sum of the segments of the base is to the sum of the sides as the difference of the sides to the difference of the segments of the base. Q, ED PROP. VI. In any triangle, twice the rectangle contained by any two sides is to the difference... | |
 | 1821 - 708 σελίδες
...the two opposite angles to the tangent 'of half their difference (by art. 59, Geom.) THEOREM IV. As the base of any plane triangle is to the sum of the two sides, so is the difference of the two sides to twice the distance of a perpendicular (let fall upon tht base from the opposite angle)... | |
 | Robert Gibson - 1821 - 594 σελίδες
...EF. But (by theo. 17. sect. 4.) FD x AD = GD x HD, hence FD : GD : : HD . AD. That is, as the base, is to the sum of the two sides; so is the difference of the sides, to the sum of the segments of the base. QED Cor. 2. Hence, (by calling any side the base) the base, is to... | |
 | Peter Nicholson - 1823 - 210 σελίδες
...perpendicular be drawn from an angle of a triangle, to the opposite side, which is the base ; then, as the base is to the sum of the two sides, so is the difference...sides to the difference of the segments of the base. For, (theorem 62, page 56) AC*-CD*=AD* and, again, (theorem 62) BC*- CD*=BD*. Subtract the second equation... | |
 | Nathaniel Bowditch - 1826 - 732 σελίδες
...the two opposite angles to the tangent 'tif half their difference (by art. u'J, Geom.) THEOREM IV. As the base of any plane triangle is to the sum of the two sides, so is the difference of the two sides to twice the distance of a perpendicular (let fall upon the *basefrom the opposite angle)... | |
 | Pierce Morton - 1830 - 584 σελίδες
...the base, or of the base produced, may be stated thus : — the base is to the sum of the sides as the difference of the sides to the difference of the segments of the base, or sum of the segments of the base produced. For it is shown (1. 38.) that the difference of the squares... | |
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... the sum of the segments of the base is to the sum of the sides as the difference of the sides to the difference of the segments of the base. 
