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" THEN, IF THE SEGMENT BE LESS THAN A SEMI-CIRCLE, SUBTRACT THE AREA OF THE TRIANGLE FROM THE AREA OF THE SECTOR. "
A Practical Application of the Principles of Geometry to the Mensuration of ... - Page 20
by Jeremiah Day - 1815 - 96 pages
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The American Arithmetic: Adapted to the Currency of the United States ...

Oliver Welch - Arithmetic - 1812 - 236 pages
...to measure whteh.. measure the sector ABCD by case 11, and also meus 02 r ure the triangle ADC, and subtract the area of the triangle from the area of the sector ; and the remainder will be tiie area of the segment AB C. \ Examples. » \. What is the area of the...
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Hawney's Complete Measurer: Or, The Whole Art of Measuring: Being a Plain ...

William Hawney - Geometry - 1820 - 336 pages
...whole sector CADBC by Section XII. and then (by Section V.) find the area of the triangle ABC, and subtract the area of the triangle from the area of the sector, the remainder will be the area of the segment. If the segment be greater than a semicircle, add the...
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A New and Concise System of Arithmetick: Containing Vulgar, Decimal, and ...

Beriah Stevens - Arithmetic - 1822 - 436 pages
...and perpendicular height 34, found by subtracting the versed sine BD from half the diameter ; then subtract the area of the triangle from the area of the sector, and the remainder will be the area of the segment ABC. See the work. 104=BC B 2 208 172= 12 208 add....
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The Second [-fifth and Sixth] Part of A Course of Mathematics: Adapted to ...

Jeremiah Day - Geometry - 1824 - 440 pages
...ALSO THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN, w THE SEGMENT BE LESS THAN A SEMI-CIRCLE, SUBTRACT THE...AREA OF THE TRIANGLE FROM THE AREA OF THE SECTOR. BlJT, IF THE SEGMENT BE GREATER THAN A SEMI-CIRCLE, ADD THE AREA OF THE TRIANGLE TO THE AREA OF THE...
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Connolly's Arithmetic: Or, The Ohio Accomptant: Being a Plain Practical ...

James L. Connolly (mathematician.) - Arithmetic - 1829 - 266 pages
...and multiply the half chord by the perpendicular, and the product is the area of the triangle. Then subtract the area of the triangle from the area of the sector, and the remainder is the area of the segment. Let it be required to find the area of the segment of...
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The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying

Jeremiah Day - Measurement - 1831 - 520 pages
...ARC, AND ALSO THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN, IF THE SEGMENT BE LESS THAN A SEMI-CIRCLE, SUBTRACT...AREA OF THE TRIANGLE FROM THE AREA OF THE SECTOR. BlJT, IF THE SEGMENT BE GREATER THAN A SEMI-CIRCLE, ADD THE AREA OF THE TRIANGLE TO THE AREA OF THE...
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The Western Arithmetic: Or, Pennsylvania and Ohio Accomptant: Being a Plain ...

James L. Connolly (mathematician.) - Arithmetic - 1835 - 264 pages
...and multiply the half chord by the perpendicular, and the product is the area of the triangle. Then subtract the area of the triangle from the area of the sector, and the remainder is the area of the segment. Let it be required to find the area of the segment of...
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The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying ...

Jeremiah Day - Measurement - 1836 - 418 pages
...SECTOR WHICH HAS THE SAME ARC, AND ALSO THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEOMENT AND THE RADII OF THE SECTOR. I THEN, IF THE SEGMENT...the sector AOBC, it is evident the difference will he the segment AOBP, less than a semi-circle. And if the same triangle be added to the sector ADBC,...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...and also the area of the triangle formed by the chord of the segment, and the radii of the sector. Then, if the segment be less than a semicircle, subtract...be greater than a semicircle, add the area of the trian, gle to the area of the sector. To find the area of a circular zone. From the area of the whole...
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Geometry: Applied to the Mensuration of Lines, Surfaces, Solids, Heights and ...

B[enjamin] Franklin Callender - Measurement - 1836 - 226 pages
...19.4X2=36.8, the area of the triangle ABC. 126.126—38.8=37.326, area of the segment ADC. If the segment is greater than a semicircle, add the area of the triangle to the area of the sector. Length of the arc ABC 64.704. Half the radius 8.5. 64.704X8.5=549.984, the area of the sector ABC D....
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