Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Seite 109
... decagon . Let AB be the straight line , on which it is required to describe a regular decagon . On AB construct ( IV . 4. ) an isosceles triangle having each of the angles at its base double of the vertical angle , and , about the point ...
... decagon . Let AB be the straight line , on which it is required to describe a regular decagon . On AB construct ( IV . 4. ) an isosceles triangle having each of the angles at its base double of the vertical angle , and , about the point ...
Seite 119
... decagon in a given circle . Let ADH be a circle , in which it is required to inscribe a regular decagon . Draw the radius OA , and with OA as its side describe the isosceles triangle AOB , having each of its angles at the base double of ...
... decagon in a given circle . Let ADH be a circle , in which it is required to inscribe a regular decagon . Draw the radius OA , and with OA as its side describe the isosceles triangle AOB , having each of its angles at the base double of ...
Seite 120
... decagon and a pentagon may be circum- scribed about the circle , by applying tangents at their se- veral angular ... decagon . Let ABCDEF be half of a decagon inscribed in a cir- cle whose diameter is AF ; the square of AC , the side of ...
... decagon and a pentagon may be circum- scribed about the circle , by applying tangents at their se- veral angular ... decagon . Let ABCDEF be half of a decagon inscribed in a cir- cle whose diameter is AF ; the square of AC , the side of ...
Seite 121
... decagon . Cor . The triple chord AD of the decagon is equal to the combined sides AO and AB of the inscribed hexa- gon and decagon . For the triangle OAG , being equal to AOB or COD , the angle DCO or DCG is equal to AGO or DGC , and ...
... decagon . Cor . The triple chord AD of the decagon is equal to the combined sides AO and AB of the inscribed hexa- gon and decagon . For the triangle OAG , being equal to AOB or COD , the angle DCO or DCG is equal to AGO or DGC , and ...
Seite 122
... decagon , and AD the side of a hexagon inscribed ; the arc BD will be the fifteenth part of the circumference of the circle , and DC the thirtieth part . 30 For , if the circumference were divided into thirty equal portions , the arc AB ...
... decagon , and AD the side of a hexagon inscribed ; the arc BD will be the fifteenth part of the circumference of the circle , and DC the thirtieth part . 30 For , if the circumference were divided into thirty equal portions , the arc AB ...
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Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ... University Professor Emeritus John Leslie, Sir Keine Leseprobe verfügbar - 2016 |
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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.