Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added Elements of Plane and Spherical TrigonometryW. E. Dean, 1851 - 317 σελίδες |
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Σελίδα 6
... given in numbers . A Geometrical solution , is the answer given by the principles of Geome- try . And a Mechanical solution , is one obtained by trials . 10. A Lemma is a preparatory proposition , laid down in order to shorten the ...
... given in numbers . A Geometrical solution , is the answer given by the principles of Geome- try . And a Mechanical solution , is one obtained by trials . 10. A Lemma is a preparatory proposition , laid down in order to shorten the ...
Σελίδα 12
... given straight line ; it is required to describe an equi- lateral triangle upon it . From the centre A , at the dis ... given straight line AB . PROP . II . PROB . From a given point to draw a straight line equal to a given straight line ...
... given straight line ; it is required to describe an equi- lateral triangle upon it . From the centre A , at the dis ... given straight line AB . PROP . II . PROB . From a given point to draw a straight line equal to a given straight line ...
Σελίδα 13
... given point A , a straight line AL has been drawn equal to the given straight line BC . PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two given straight lines ...
... given point A , a straight line AL has been drawn equal to the given straight line BC . PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two given straight lines ...
Σελίδα 17
... given rectilineal angle , that is , to divide it into two equal angles . A Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D in AB , and from AC cut ( 3. 1. ) off AE equal to AD ; join DE , and upon ...
... given rectilineal angle , that is , to divide it into two equal angles . A Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D in AB , and from AC cut ( 3. 1. ) off AE equal to AD ; join DE , and upon ...
Σελίδα 18
... given straight line , from a given point in that line . Let AB be a given straight line , and C a point given in it ; it is requi- red to draw a straight line from the point C at right angles to AB . F Take any point Ď in AC , and ( 3 ...
... given straight line , from a given point in that line . Let AB be a given straight line , and C a point given in it ; it is requi- red to draw a straight line from the point C at right angles to AB . F Take any point Ď in AC , and ( 3 ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore