The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner Corrected |
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Page 7
... meet together , but are not in the same direction . " IX . A plane rectilineal angle is the inclination of two straight lines to one another , which meet together , but are not in the same straight line . • See Notes . A D B C E N. B. ...
... meet together , but are not in the same direction . " IX . A plane rectilineal angle is the inclination of two straight lines to one another , which meet together , but are not in the same straight line . • See Notes . A D B C E N. B. ...
Page 8
... meet one another , is put ' between the other two letters , and one of these two is some- ' where upon one of those straight lines , and the other upon ' the other line : Thus the angle which is contained by the straight lines AB , CB ...
... meet one another , is put ' between the other two letters , and one of these two is some- ' where upon one of those straight lines , and the other upon ' the other line : Thus the angle which is contained by the straight lines AB , CB ...
Page 11
... meet . POSTULATES . I. Let it be granted that a straight line may be drawn from any one point to any other point . II . That a terminated straight line may be produced to any length in a straight line . 1 III . And that a circle may be ...
... meet . POSTULATES . I. Let it be granted that a straight line may be drawn from any one point to any other point . II . That a terminated straight line may be produced to any length in a straight line . 1 III . And that a circle may be ...
Page 12
... meet two straight lines , so as to make the two " interior angles on the same side of it taken together less " than two right angles , these straight lines being continual- " ly produced , shall at length meet upon that side on which ...
... meet two straight lines , so as to make the two " interior angles on the same side of it taken together less " than two right angles , these straight lines being continual- " ly produced , shall at length meet upon that side on which ...
Page 32
... meet to- wards B , D. In like manner it may be demonstrated that they do not meet towards A , C F E B G D C ; but those straight lines which meet neither way , though produced ever so far , are parallel ( 35. def . ) to one another . AB ...
... meet to- wards B , D. In like manner it may be demonstrated that they do not meet towards A , C F E B G D C ; but those straight lines which meet neither way , though produced ever so far , are parallel ( 35. def . ) to one another . AB ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2018 |
Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference co-sine cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Popular passages
Page 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 81 - The angles in the same segment of a circle are equal to one another.
Page 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Page 33 - 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.
Page 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Page 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Page 155 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 22 - ANY two angles of a triangle are together less than two right angles.
Page 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Page 24 - Any two sides of a triangle are together greater than the third side.