. Asiatic Researches. Reducing Practical Tables and Calculations. m? If we ufe the fecond and third'proportions, putting two and three for-. in and -n, and for a and b, three-halves and two; in the full cafe j .and-. one-half and-one, in-the feeond we ^et the-fame values; â Hence in general r+ i r' râi- r t x -fc ââ N ;.N «.- x : : x : N- «x X. 2 ' % â Another example of the advantage of transferring practices from one fub- ject to another is this. L>r. Halley has applied a method fimilar to that" of interpolation to mid the time of the tropicks : now the fun's meridian alti Lide may
. Asiatic Researches. Reducing Practical Tables and Calculations. m? If we ufe the fecond and third'proportions, putting two and three for-. in and -n, and for a and b, three-halves and two; in the full cafe j .and-. one-half and-one, in-the feeond we ^et the-fame values; â Hence in general r+ i r' râi- r t x -fc ââ N ;.N «.- x : : x : N- «x X. 2 ' % â Another example of the advantage of transferring practices from one fub- ject to another is this. L>r. Halley has applied a method fimilar to that" of interpolation to mid the time of the tropicks : now the fun's meridian alti Lide may be found in the fame way from altitudes taken near the meri- dian, and-if the obferver begins a little before noon to take altitudes and the times, and continues to do fo till a little afternoon, a number of meridian altitude's may be deduced from thefe, and the latitude found much more ex- actly from them, than can be expected from a fmgle meridian altitude, b^ uungjthe exprefhon forthe maximum, or othervvife; ⢠Analogous to theTe, are methods of generalizing properties from particular cafes : thus, if Ab Ac be" tangents to a circle, and -if any lines BG, be, be alfo' drawn to touch, thccircle j then^ the perimeters of all the triangles ABC, will-be conftant, and alfo the dif- ference between the fum of Ab and Ac and the bafe be: this property is- of uncommon' ufe-in the coftftruc^ tion of problems relative to plain triangles and trape- ziums j and if lines be fuppofed drawn from the centre, m a point in the circumference of a fphercy to each: part of the figure, it will be found, that the projection of the figure upon the fphere will have analogo>is properties, and that the theorem is alfo true in fpherical triangles. By a like mode of confideration, problems fimilar tothofe ofâ Apcllo^i r s. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illu
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Keywords: ., bookcentury1700, bookdecade1790, bookpublishercalcu, bookyear1792
