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 TrigonometryLippincott, Grambo & Company, 1854 - 317 σελίδες |
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Σελίδα 8
... straight line . " " COR . Hence two straight lines cannot inclose a space . Neither can two straight lines have a common segment ; that is , they cannot coincide " in part , without coinciding altogether . " 66 4. A superficies is that ...
... straight line . " " COR . Hence two straight lines cannot inclose a space . Neither can two straight lines have a common segment ; that is , they cannot coincide " in part , without coinciding altogether . " 66 4. A superficies is that ...
Σελίδα 9
... straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right angle ; and the straight line which stands on the other , is called a perpendicu- lar to it . 8. An ...
... straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right angle ; and the straight line which stands on the other , is called a perpendicu- lar to it . 8. An ...
Σελίδα 11
... straight lines are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . 1. LET it be granted that a straight line ... straight line may be produced to any length in a straight line . 3 ...
... straight lines are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . 1. LET it be granted that a straight line ... straight line may be produced to any length in a straight line . 3 ...
Σελίδα 12
... straight line . Let AB be the given straight line ; it is required to describe an equi . lateral triangle upon it . From the centre A , at the dis- tance AB , describe ( 3. Postulate ) the circle BCD , and from the cen- tre B , at the ...
... straight line . Let AB be the given straight line ; it is required to describe an equi . lateral triangle upon it . From the centre A , at the dis- tance AB , describe ( 3. Postulate ) the circle BCD , and from the cen- tre B , at the ...
Σελίδα 13
... straight line AL is equal to BC . Wherefore , from the 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 ...
... straight line AL is equal to BC . Wherefore , from the 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 ...
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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