Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 σελίδες |
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Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 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 ...
... 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 ...
Σελίδα 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 ...
Σελίδα 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 . 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 . For , if the circumference were divided into thirty equal portions , the arc AB ...
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Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ... University Professor Emeritus John Leslie, Sir Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angle altitude angle ABC angle ADB angle BAC angle BCD 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 greater half Hence hypotenuse inscribed intercepted 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 sinAC sinB sine square of AB square of AC tangent THEOR tion triangle ABC twice the rectangle twice the square vertex vertical angle whence Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 30 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Σελίδα 333 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...
Σελίδα 294 - 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...
Σελίδα 10 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 137 - Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth.
Σελίδα 84 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.
Σελίδα 292 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
Σελίδα 93 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
Σελίδα 38 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 58 - The rectangle contained by the sum and difference of two straight lines is equivalent to the difference of the squares of these lines.