 | Edward Riddle - Nautical astronomy - 1824 - 572 pages
...the first case. 3. When the three sides are given to find the angles. As the base, or longest side, is to the sum of the other two sides, so is the difference...sides to the difference of the segments of the base, made by a perpendicular from the opposite angle, (Trig. Prop. 7.) Then the half difference added to... | |
 | Abel Flint - Surveying - 1825 - 252 pages
...solution of this CASE depends on the following PROPOSITION. In every Plane Triangle, as the longest Side is to the sum of the other two Sides, so is the difference between those two Sides to the difference between the Segments of the longest Side, made by a Perpendicular... | |
 | Arithmetic - 1829 - 196 pages
...after the FOLLOWING MANNER : 349 a. As the WHOLE BASE : is to the BUM OF THE TWO SHOBTEI •iiDEB : : so is the DIFFERENCE of those sides : to the DIFFERENCE OF THE * The longest side of a triangle is usually called the hase, except in a right an glcd triangle, where... | |
 | Charles Hutton - Mathematics - 1831 - 660 pages
...triangle into two right-angled triangles : then the proportion will be, As the base, or sum of the segments, Is to the sum of the other two sides ; So is ihe difference of those sides, To the «lilK of the segments of the base. Then take half this difference... | |
 | Tobias Ostrander - Measurement - 1833 - 172 pages
...angles, or the diameter of a circle circumscribing the triangle. Rule—As the whole length of the base is to the sum of the other two sides, so is the difference...sides to the difference of the segments of the base; half the said difference added to half the base gives the greater of the two segments, subtracted leaves... | |
 | Tobias Ostrander - Measurement - 1834 - 182 pages
...perpendicular which will divide it into two right angles. Rule — As the whole length of the base is to the sum of the other two sides, so is the difference...sides to the difference of the segments of the base ; half the said difference added to half the base, gives the longest of the two segments — subtracted,... | |
 | Abel Flint - Geometry - 1835 - 368 pages
...solution of this CASE depends on the following PROPOSITION. IN EVERY PLANE TRIANGLE, AS THE LONGEST SIDE IS TO THE SUM OF THE OTHER TWO SIDES, SO IS THE DIFFERENCE BETWEEN THOSE TWO SIDES TO THE DIFFERENCE BETWEEN THE SEGMENTS OF THE LONGEST SIDE, MADE BY A PERPENDICULAR... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...base ; the sum of the segments of the base is to the sum of the other tioo sides of the triangle as the difference of those sides to the difference of the segments of the base. For (K. 6.), the rectangle under the sum and difference of the segments of the base is equal to the... | |
 | Thomas Holliday - Surveying - 1838 - 404 pages
....»177.5. Case 3rd. When the three sides are given to find the angles. Rule.—As the base or greatest side is to the sum of the other two sides, so is the difference of the sides to the difference of the segments of the base made by a perpendicular, let fall from the... | |
 | John Gummere - Surveying - 1840 - 450 pages
...the whole triangle into two rightangled triangles. Then, As the base, or sum of the segments, Is io the sum of the other two sides ; So is the difference...sides, To the difference of the segments of the base.* * DEKomrRATiON. Let ABC, Fig. 48, be a triangle, and CD be perpendicular upon AH. About C as a centre... | |
| |
As the base or sum of the segments Is to the sum of the other two sides, So is the difference of those sides To the difference of the segments of the base. 
