The Elements of Euclid; viz. the first six books,together with the eleventh and twelfth, with an appendix |
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Page 17
... 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 any length both ways , and let C be a point without it . It is required to draw ...
... 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 any length both ways , and let C be a point without it . It is required to draw ...
Page 18
... perpendicular to it ; therefore from the given point C a perpendicular CH has been drawn to the given straight line AB . Which was to be done . PROP . XIII . THEOR . The angles which one straight line makes with another upon one side of ...
... perpendicular to it ; therefore from the given point C a perpendicular CH has been drawn to the given straight line AB . Which was to be done . PROP . XIII . THEOR . The angles which one straight line makes with another upon one side of ...
Page 62
... perpendicular falls , and the straight line intercepted without the triangle between the perpendicular and the obtuse angle . Let ABC be an obtuse - angled triangle , having the · obtuse angle ACB , and from the point A let 62 EUCLID'S ...
... perpendicular falls , and the straight line intercepted without the triangle between the perpendicular and the obtuse angle . Let ABC be an obtuse - angled triangle , having the · obtuse angle ACB , and from the point A let 62 EUCLID'S ...
Page 63
... perpendicular to BC produced : the square of * 12. 1 . AB shall be greater than the squares of AC , CB , by twice ... perpendicular let fall upon it from the opposite angle . Let ABC be any triangle , and the angle at B one of its ...
... perpendicular to BC produced : the square of * 12. 1 . AB shall be greater than the squares of AC , CB , by twice ... perpendicular let fall upon it from the opposite angle . Let ABC be any triangle , and the angle at B one of its ...
Page 65
Euclides William Rutherford. Lastly , let the side AC be perpendicular to BC ; then BC is the straight line be- tween the perpendicular and the acute angle at B ; and it is manifest that the squares of AB , BC , are equal to the square ...
Euclides William Rutherford. Lastly , let the side AC be perpendicular to BC ; then BC is the straight line be- tween the perpendicular and the acute angle at B ; and it is manifest that the squares of AB , BC , are equal to the square ...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
Common terms and phrases
AB is equal AC is equal altitude angle ABC angle ACB angle BAC base BC bisect centre circle ABCD circle EFGH circumference common section cone cylinder demonstrated described diameter draw equal to F equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prisms PROB proved pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD sphere square of AC straight line AC THEOR third three plane angles three straight lines tiples touches the circle triangle ABC triangle DEF triplicate ratio twice the rectangle wherefore whole
Popular passages
Page 173 - 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 56 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 53 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Page 58 - IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Page 94 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Page 23 - Any two sides of a triangle are together greater than the third side.
Page 40 - EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels.
Page 103 - 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 on the line which touches it.
Page 50 - PROP. I. THEOR. If there oe two straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Page 28 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.