Elements of Geometry and Trigonometry |
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Page 41
... and is formed by two chords . B an arc . The chord , or subtense of an arc , is the straight line FG , which joins its two extremities . † 4. A segment is the surface or portion of a circle , included between an arc and its chord .
... and is formed by two chords . B an arc . The chord , or subtense of an arc , is the straight line FG , which joins its two extremities . † 4. A segment is the surface or portion of a circle , included between an arc and its chord .
Page 55
All the angles BAC , BDC , BEC , inscribed in the same segment are equal ; because they are all measured by the half of the same arc BOC . B Cor . 2. Every angle BAD , inscribed in a semicircle is a right angle ; because it is measured ...
All the angles BAC , BDC , BEC , inscribed in the same segment are equal ; because they are all measured by the half of the same arc BOC . B Cor . 2. Every angle BAD , inscribed in a semicircle is a right angle ; because it is measured ...
Page 65
A On a given straight line to describe a segment that shall contain a given angle ; that is to say , a segment such , that all the angles inscribed in it , shall be equal to the given angle . Let AB be the given straight line , and C ...
A On a given straight line to describe a segment that shall contain a given angle ; that is to say , a segment such , that all the angles inscribed in it , shall be equal to the given angle . Let AB be the given straight line , and C ...
Page 66
If the given angle were a right angle , the required segment would be a semicircle , described on AB as a diameter . PROBLEM XVII . To find the numerical ratio of two given straight lines , these lines being supposed to have a common ...
If the given angle were a right angle , the required segment would be a semicircle , described on AB as a diameter . PROBLEM XVII . To find the numerical ratio of two given straight lines , these lines being supposed to have a common ...
Page 68
In two different circles , similar arcs , sectors , or segments , are those which correspond to equal angles at the centre . ... the sector BAC to the sector DOE , and the segment whose chord is BC , to the seg ment whose chord is DE .
In two different circles , similar arcs , sectors , or segments , are those which correspond to equal angles at the centre . ... the sector BAC to the sector DOE , and the segment whose chord is BC , to the seg ment whose chord is DE .
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ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole