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 194
... SOLID is that which hath length , breadth , and thickness . II . That which bounds a solid is a superficies . III . A straight line is perpendicular , or at right angles to a plane , when it makes right angles with every straight line ...
... SOLID is that which hath length , breadth , and thickness . II . That which bounds a solid is a superficies . III . A straight line is perpendicular , or at right angles to a plane , when it makes right angles with every straight line ...
Page 195
... solid angle is that which is made by the meeting of more than two plane angles , which are not in the same plane , in one point . * X. ' The tenth definition is omitted for reasons given in the notes . ** XI . Similar solid figures are ...
... solid angle is that which is made by the meeting of more than two plane angles , which are not in the same plane , in one point . * X. ' The tenth definition is omitted for reasons given in the notes . ** XI . Similar solid figures are ...
Page 196
... angle , which revolves . XXI . A cylinder is a solid figure described by the revolution of a right angled parallelogram about one of its sides , which remains fixed . XXII . The axis of a cylinder is the fixed straight line about which ...
... angle , which revolves . XXI . A cylinder is a solid figure described by the revolution of a right angled parallelogram about one of its sides , which remains fixed . XXII . The axis of a cylinder is the fixed straight line about which ...
Page 210
... angles to the other plane ( 4. def . 11. ) : and any straight line FG in the plane DE , which is at right angles to CE the common section of the planes , has been proved to be ... solid angle 210 BOOK XI . THE ELEMENTS OF EUCLID .
... angles to the other plane ( 4. def . 11. ) : and any straight line FG in the plane DE , which is at right angles to CE the common section of the planes , has been proved to be ... solid angle 210 BOOK XI . THE ELEMENTS OF EUCLID .
Page 211
... solid angle be contained by three plane angles , any two of them are greater than the third . * Let the solid angle at A be contained by the three plane an- gles , BAC , CAD , DAB . Any two of them are greater than the third . D If the ...
... solid angle be contained by three plane angles , any two of them are greater than the third . * Let the solid angle at A be contained by the three plane an- gles , BAC , CAD , DAB . Any two of them are greater than the third . D If the ...
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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.