Elements of Geometry and Trigonometry |
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Page 30
... in the polygon : hence the sum of all the angles of the polygon is equal to two right angles , taken as many times as there are triangles in the figure ; in other words , as there are units in the number of sides diminished by two .
... in the polygon : hence the sum of all the angles of the polygon is equal to two right angles , taken as many times as there are triangles in the figure ; in other words , as there are units in the number of sides diminished by two .
Page 34
If the other magnitude contain a certain number of those units , it also may be expressed by the number of its units ... If the second magnitude do not contain the measuring unit an exact number of times , there may perhaps be a smaller ...
If the other magnitude contain a certain number of those units , it also may be expressed by the number of its units ... If the second magnitude do not contain the measuring unit an exact number of times , there may perhaps be a smaller ...
Page 53
It appears most natural to measure a quantity by a quantity of the same species ; and upon this principle it would be convenient to refer all angles to the right angle ; which , being made the unit of measure , an acute angle would be ...
It appears most natural to measure a quantity by a quantity of the same species ; and upon this principle it would be convenient to refer all angles to the right angle ; which , being made the unit of measure , an acute angle would be ...
Page 69
3 cally by the number of times which the figure contains some other area , that is assumed for its measuring unit . 9. Figures have equal areas , when they contain the same measuring unit an equal number of times . 10.
3 cally by the number of times which the figure contains some other area , that is assumed for its measuring unit . 9. Figures have equal areas , when they contain the same measuring unit an equal number of times . 10.
Page 72
This product will give the number of superficial units in the surface ; because , for one unit in height , there are as many superficial units as there are linear units in the base ; for two units in height twice as many ; for three ...
This product will give the number of superficial units in the surface ; because , for one unit in height , there are as many superficial units as there are linear units in the base ; for two units in height twice as many ; for three ...
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Common terms and phrases
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