The Elements of Euclid; viz. the first six books,together with the eleventh and twelfth, with an appendix |
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... demonstrated truth . Whenever an inference is con- trary to a demonstrated truth , the language of Simson is frequently ambiguous , and does not clearly point out whether the inference or the demonstrated truth is im- possible . In ...
... demonstrated truth . Whenever an inference is con- trary to a demonstrated truth , the language of Simson is frequently ambiguous , and does not clearly point out whether the inference or the demonstrated truth is im- possible . In ...
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... demonstrated by the student , in strict conformity with the language of the enunciation of the Proposition . The demonstration of the First Proposition of the Third Book has been long known to be defective , and it is here rendered ...
... demonstrated by the student , in strict conformity with the language of the enunciation of the Proposition . The demonstration of the First Proposition of the Third Book has been long known to be defective , and it is here rendered ...
Page 11
... demonstrated . PROP . V. THEOR . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles ...
... demonstrated . PROP . V. THEOR . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles ...
Page 12
... demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; the remaining angle ABC is therefore equal to the remaining angle ACB , which are the angles at the base of ...
... demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; the remaining angle ABC is therefore equal to the remaining angle ACB , which are the angles at the base of ...
Page 19
... demonstrated to be equal to the same three angles ; and things that are equal to the same thing are equal to one another ; * 1 Ax . therefore the angles CBE , EBD are equal to the angles DBA , ABC ; but CBE , EBD are two right angles ...
... demonstrated to be equal to the same three angles ; and things that are equal to the same thing are equal to one another ; * 1 Ax . therefore the angles CBE , EBD are equal to the angles DBA , ABC ; but CBE , EBD are two right angles ...
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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.