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In a right angled spherical triangle, the rectangle under the radius and the sine of the middle part, is equal to the rectangle under the tangents of the adjacent parts ; or', to the rectangle under the cosines of the opposite parts.
Trigonometry, Plane and Spherical: With the Construction and Application of ... - Page 28
by Thomas Simpson - 1810 - 125 pages

## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...contained in the following " * PROPOSITION. In a right angled spherical triangle, the rectangle under the radius and the sine of the middle part, is equal to the rettangle under the tangents of the adjacent parts ; or to the rectangle under the cosines of the opposite,...

## Principles of Education, Intellectual, Moral, and Physical

Lant Carpenter - Education - 1820 - 514 pages
...for the solution of right-angled spherical triangles. Here the short sentence, " the rectangle of the radius and the sine of the middle part, is equal to the rectangle of the tangents of the extremes conjunct, or, of the cosines of the extremes disjunct," enables the calculator...

## New American Practical Navigator

Nautical astronomy - 1821 - 706 pages
...„';,, '„_ These equations, when applied to-right-angled spheric triangles, signify as before thtit the sine of the middle part is equal to the rectangle of the tangents of the adjacent parts, or to the rectangle of the co-sines of the opposite parts ; but when...

## Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - Astronomy - 1822 - 516 pages
...under the cosines of AB and AC. PROP. XXIV. THEOR. The same things being supposed, the rectangle under radius and the sine of the middle part, is equal to the rectangle under the tangents of the parts, which, the right angle being excluded, are adjacent to the middle...

## Dictionary of the Mathematical and Physical Sciences, According to the ...

James Mitchell - Mathematics - 1823 - 666 pages
...anplesof aright angled spherical triangle. Napier's general rule is this: the rectangle, under the radius and the sine of the middle part, is equal to the rectangle under the tangents of the adjacent parts, and to the rectangle under the cosines of the opposite parts....

## A treatise on navigation, and nautical astronomy

Edward Riddle - Nautical astronomy - 1824 - 572 pages
...terms, Napier's Rules for the solution of the different cases of right angled spherical triangles are 1. The rectangle of radius and the sine of the middle part is equal to the rectangle of the tangents of the adjoining extremes. 2. The rectangle of radius and the sine of the middle part is equal...

## The New American Practical Navigator: Being an Epitome of Navigation ...

Nathaniel Bowditch - Nautical astronomy - 1826 - 732 pages
...parts. , ''These equations, when applied to right-angled «phenc triangles, signify as before, H. that the sine of the middle part is equal to the rectangle of the tangents of the adjacent parts, 01 to the rectangle of the co-eiiies of the opposite parts : but when...

## The New American Practical Navigator: Being an Epitome of Navigation ...

Nathaniel Bowditch - Nautical astronomy - 1826 - 782 pages
...Sine П1Ш< „art These equations, when applied to right-angled spheric triangles, signify as that the sine of the middle part is equal to the rectangle of the tangents of the ¡ parts, or to the rectangle of the co-sines of the opposite parts ; but when appui...