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" Prove that, in any plane triangle, the base is to the difference of the other two sides, as the sine of half the sum of the angles at the base, to the sine of half their difference : also, that the... "
A Course of Mathematics: In Three Volumes : Composed for the Use of the ... - Page 72
by Charles Hutton - 1811
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A Course of Mathematics for the Use of Academies: As Well as ..., Volume 2

Charles Hutton - 1826 - 682 pages
...sine and versed sine of an arc, is equal to the square of double the sine of half the arc. Ex. 11. Demonstrate that the sine of an arc is a mean proportional...that the base is to the sum of the other two sides at as the cosine of half the sum of the angles at the base, to the cosine of half their difference....
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 546 pages
...PROP. III. FIG. 8. In a plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. Let ABC be a plane triangle, the sum of any two sides AB, AC will...
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A Course of Mathematics: For the Use of Academies as Well as ..., Volume 2

Charles Hutton - 1831 - 656 pages
...sine and versed sine of an arc, is equal to the square of double the sine of half the arc. Ex. 11. Demonstrate that the sine of an arc is a mean proportional...sides, as the sine of half the sum of the angles at the hasp., to tlio aino of half their difference : also, that the base is to the sum of the other two sides,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...PROP. III. FIG. 8. In a plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. Let ABC be a plane triangle, the sum of any two sides AB, AC will...
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The Element of Geometry

John Playfair - 1836 - 148 pages
...5.) EC is to CF, as EB to BG; that is, the sum of the sides is to their difference, as the tangent of half the sum of the angles at the base to the tangent of half their difference. PROP. IV. In any plane triangle BAC, whose two sides are BA, AC,...
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Elements of Plane Geometry According to Euclid

Andrew Bell, Robert Simson - 1837 - 290 pages
...vertical angle is divided. 2. The base of a triangle is to the sum of its two sides, as the cosine of half the sum of the angles at the base to the cosine of half their difference. 3. The base of a triangle is to the difference of its sides, as the...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 444 pages
...their difference. Also, that the sum of the sides, is to the lifference of the segments of the base, as the sine of half the sum of the angles at the base, is to the sine of half :heir difference. APPLICATION OF PLANE TRIGONOMETRY TO THE MENSURATION OF HEIGHTS...
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - 1845 - 506 pages
...sine of half their difference : also, that the base is to the sum of the other two sides as the cosine of half the sum of the angles at the base, to the cosine of half their difference. Ex. 10. How must three trees, A, B, C, be planted, so that the angle...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - 1845 - 542 pages
...of half their difference : also-, that the base is to the sum of the other two sides as the cosine of half the sum of the angles at the base, to the cosine of half their difference. Ex. 10. How must three trees, A, B, C, be planted, so that the angle...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...sine of half their difference: also, that the base is to the sum of the other two sides as the cosine of half the sum of the angles at the base, to the cosine of half their difference. Ex. 10. How must three trees, A, B, C, be planted, so that the angle...
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