The Elements of Euclid; viz. the first six books,together with the eleventh and twelfth, with an appendix |
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Page 5
... besides these , is called a trapezium . XXXV . Parallel straight lines are such as are in the saine plane , and which , however far produced either way , do not meet . POSTULATES . I. Let it be granted , that a B 2 BOOK I. - DEFINITIONS .
... besides these , is called a trapezium . XXXV . Parallel straight lines are such as are in the saine plane , and which , however far produced either way , do not meet . POSTULATES . I. Let it be granted , that a B 2 BOOK I. - DEFINITIONS .
Page 30
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD make the alternate angles AEF , EFD equal to one another ; AB shall be parallel to CD . For , if AB be not parallel to CD , AB and CD being produced ...
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD make the alternate angles AEF , EFD equal to one another ; AB shall be parallel to CD . For , if AB be not parallel to CD , AB and CD being produced ...
Page 31
... parallel to CD . Because the angle EGB is equal * E * Hyp . to the * 15. 1 . Hyp . 13. 1 . to the angle GHD , and the angle EGB equal angle AGH , therefore the angle AGH is equal to the angle GHD ; and they are alternate angles ...
... parallel to CD . Because the angle EGB is equal * E * Hyp . to the * 15. 1 . Hyp . 13. 1 . to the angle GHD , and the angle EGB equal angle AGH , therefore the angle AGH is equal to the angle GHD ; and they are alternate angles ...
Page 32
... parallel to the same straight line are parallel to each other . Let AB , CD be each of them parallel to EF ; AB shall be parallel to CD . Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the parallel straight lines AB ...
... parallel to the same straight line are parallel to each other . Let AB , CD be each of them parallel to EF ; AB shall be parallel to CD . Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the parallel straight lines AB ...
Page 33
... parallel to BC . * 27. 1 . Therefore the straight line EAF is drawn through the given point A , parallel to the given straight line BC . Which was to be done . PROP . XXXII . THEOR . If a side of any triangle be produced , the exterior ...
... parallel to BC . * 27. 1 . Therefore the straight line EAF is drawn through the given point A , parallel to the given straight line BC . Which was to be done . PROP . XXXII . THEOR . If a side of any triangle be produced , the exterior ...
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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.