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 CorrectedDesilver, 1829 - 516 sider |
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Side 8
... perpendicular to it . XI . An obtuse angle is that which is greater than a right angle . XII . An acute angle is that which is less than a right angle . XIII . " A term or boundary is the extremity of any thing . " XIV . figure is that ...
... perpendicular to it . XI . An obtuse angle is that which is greater than a right angle . XII . An acute angle is that which is less than a right angle . XIII . " A term or boundary is the extremity of any thing . " XIV . figure is that ...
Side 21
... perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight line , which may be produced to any length both ways , and let C be a point without it . It is re- quired to ...
... perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight line , which may be produced to any length both ways , and let C be a point without it . It is re- quired to ...
Side 61
... perpendicular falls , and the straight line intercepted without the trian- gle between the perpendicular and the obtuse angle . Let ABC be an obtuse angled triangle , having the obtuse an- gle ACB , and from the point A let AD be drawn ...
... perpendicular falls , and the straight line intercepted without the trian- gle between the perpendicular and the obtuse angle . Let ABC be an obtuse angled triangle , having the obtuse an- gle ACB , and from the point A let AD be drawn ...
Side 62
... perpendicular let fall upon it from the oppo- site angle , and the acute angle . * Let ABC be any triangle , and the angle at B one of its acute angles , and upon BC , one of the sides containing it , let fall the perpendicular ( 12. 1 ...
... perpendicular let fall upon it from the oppo- site angle , and the acute angle . * Let ABC be any triangle , and the angle at B one of its acute angles , and upon BC , one of the sides containing it , let fall the perpendicular ( 12. 1 ...
Side 63
... perpendicular to BC ; then is BC the straight line between the perpendi- cular and the acute angle at B ; and it is manifest that the square of AB , BC are equal ( 47. 1. ) to the square of AC and twice the square of BC . fore , in ...
... perpendicular to BC ; then is BC the straight line between the perpendi- cular and the acute angle at B ; and it is manifest that the square of AB , BC are equal ( 47. 1. ) to the square of AC and twice the square of BC . fore , in ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 81 - The angles in the same segment of a circle are equal to one another.
Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 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.
Side 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.
Side 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.
Side 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.
Side 22 - ANY two angles of a triangle are together less than two right angles.
Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Side 24 - Any two sides of a triangle are together greater than the third side.