Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Seite 226
... cosine , cotan- gent and cosecant . A farther contraction is frequently made in noting the radius and other lines connected with the circle , by retaining only the first syllable of the word , or even the mere initial letter . Let ACFE ...
... cosine , cotan- gent and cosecant . A farther contraction is frequently made in noting the radius and other lines connected with the circle , by retaining only the first syllable of the word , or even the mere initial letter . Let ACFE ...
Seite 227
... cosine of an arc are together equal to the square of the radius . 3. The triangle ODB being evidently similar to OAH , OD : DB : OA : AH ; that is , the cosine of an arc is to the sine , as the radius to the tangent . 4. From the ...
... cosine of an arc are together equal to the square of the radius . 3. The triangle ODB being evidently similar to OAH , OD : DB : OA : AH ; that is , the cosine of an arc is to the sine , as the radius to the tangent . 4. From the ...
Seite 228
... cosine . 6. Hence also the chord of an arc is a mean proportional between the versed sine and the diameter ; for AB2 = AD.AF. 7. The triangles OAH and ICO being similar , AH : OA :: OC : ' CI ; and hence the radius is a mean ...
... cosine . 6. Hence also the chord of an arc is a mean proportional between the versed sine and the diameter ; for AB2 = AD.AF. 7. The triangles OAH and ICO being similar , AH : OA :: OC : ' CI ; and hence the radius is a mean ...
Seite 229
... cosine OE ; and the sup- plemental arc ABb , and its de- F 1 fect from a whole circumference , have likewise the same cosine , although with an inverted position . AH and OH are respectively the tangent and secant not only of AB , but ...
... cosine OE ; and the sup- plemental arc ABb , and its de- F 1 fect from a whole circumference , have likewise the same cosine , although with an inverted position . AH and OH are respectively the tangent and secant not only of AB , but ...
Seite 230
... cosine shifts to the opposite side , and the secant shoots from the centre in a direction opposite to the ... cosine and secant of an arc a are equal to the cosine and secant of 2m.180 ° -a , and to the opposite cosines and secants of ...
... cosine shifts to the opposite side , and the secant shoots from the centre in a direction opposite to the ... cosine and secant of an arc a are equal to the cosine and secant of 2m.180 ° -a , and to the opposite cosines and secants of ...
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ABCD adjacent angle altitude angle ABC angle ADB angle BAC base AC bisect centre chord circle circumference consequently construction contained angle cosine decagon denote describe diameter difference distance diverging lines divided draw equal to BC equilateral triangle equivalent to twice evidently exterior angle Geometry given greater half Hence hypotenuse inscribed isosceles triangle join let fall likewise measure parallel perpendicular point G polygon PROB PROP Proposition quadrilateral figure quantities radius ratio rectangle rectangle contained rectilineal figure rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter side AC sides AB sinB sine square of AB square of AC straight line tangent THEOR tion triangle ABC twice the rectangle twice the square vertex vertical angle whence Wherefore
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Seite 22 - THEOR. Two sides of a triangle are together greater than the third side. The two sides AB and BC of the triangle ABC are together greater than the third side AC. For produce AB until DB be equal to the side BC, and join CD. Because BC is equal to BD, the angle BCD is equal to BDC (I.
Seite 292 - axiom, (If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles, these straight lines, being continually produced, will at length meet on that side on which are the angles which are less
Seite 10 - circumference. 35. The diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference. It is obvious that all radii of the same circle are equal to each other and to a
Seite 50 - PROB. With a given straight line to construct a rhomboid equivalent to a given rectilineal figure, and having an angle equal to a given angle. Let it be required to construct, with the straight line L, a rhomboid, containing a given space, and having an angle equal to K. Construct (II.
Seite 144 - Proposition is named inverse, or perturbate, equality. PROP. XIX. THEOR. If there be any number of proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. .
Seite 236 - &c. &c. PROP. IV. THEOR. The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs to the tangent of half
Seite 110 - Hence a regular twenty-sided figure may be described on a given straight line, by first constructing on it an isosceles triangle having each of the angles at the base double of the vertical angle,
Seite 30 - THEOR. If a straight line fall upon two parallel straight lines, it will make the alternate angles equal, the exterior angle equal to the interior opposite one, and the two interior angles on the same side together equal to two right angles. • Let the straight line EFG fall upon the parallels AB and CD ; the alternate angles AGF and DFG are equal, the
Seite 137 - founded the two following theorems. PROP. VII. THEOR. The terms of an analogy are proportional by inversion, or the second is to the first, as the fourth to the third. Let A : B : : C : D ; then inversely B : A : : D : C.
Seite 88 - THEOR. The angle in a semicircle is a right angle, the angle in a greater segment is acute, and the angle in a smaller segment is obtuse. Let ABD be an angle in a semicircle, or that stands on the semicircumference AED; it is a right angle.