Skeleton propositions &c. of Euclid, books i and ii, with references, by H. Green, Bind 21858 |
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Side 80
... Geometrical Reasoning , and of the application of Algebra and Arithmetic to Geometry ; secondly , that he should fill in , -not by copying from any book , but from the stores of his own mind and thought , trained by previous study of ...
... Geometrical Reasoning , and of the application of Algebra and Arithmetic to Geometry ; secondly , that he should fill in , -not by copying from any book , but from the stores of his own mind and thought , trained by previous study of ...
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... GEOMETRY , ITS USE AND APPLICATON : With an EXPLANATORY PREFACE , REMARKS ON GEOMETRICAL REASONING , and ON ARITHMETIC AND ALGEBRA APPLIED TO GEOMETRY ; PRACTICAL RESULTS and EXERCISES . PRICE 4d . EXERCISES FOR THE FIRST AND SECOND ...
... GEOMETRY , ITS USE AND APPLICATON : With an EXPLANATORY PREFACE , REMARKS ON GEOMETRICAL REASONING , and ON ARITHMETIC AND ALGEBRA APPLIED TO GEOMETRY ; PRACTICAL RESULTS and EXERCISES . PRICE 4d . EXERCISES FOR THE FIRST AND SECOND ...
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Skeleton Propositions &c. Of Euclid, Books I And Ii, With References, By H ... Euclides Ingen forhåndsvisning - 2019 |
Skeleton Propositions &c. Of Euclid, Books I And Ii, With References, By H ... Euclides Ingen forhåndsvisning - 2019 |
Skeleton Propositions &C. of Euclid, Books I and II, with References, by H ... Euclides Ingen forhåndsvisning - 2015 |
Almindelige termer og sætninger
21 Recap 9 Ax Algebra and Arithmetic Aly & Arith Area Arith COR bisected and produced BOOKS OF EUCLID Conc Concl Cone Construction and Demonstration consult the Gradations cut a line cut in extreme equal to twice equals the square EXPLANATORY PREFACE extreme and mean GEOMETRICAL REASONING GEOMETRY given rectilineal GRADATIONS IN EUCLID half the line half the square half their difference half their sum Learner Let a line line be bisected line be divided line CF line in extreme line intercepted line thus produced lines is equal mean ratio obtuse angle PEN-AND-INK EXAMINATIONS perp points of section PROP recapitulatory exercise rectangle contained references SECOND BOOKS side A B side subtending SKELETON PROPOSITIONS square of half squares is equal SYNOPSIS BK THEOR triangle truths twice the rect twice the rectangle twice the square unequal whole line
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Side 95 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Side 99 - 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 of the line between the points of section, is equal to the square of half the line.
Side 105 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Side 93 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Side 101 - IF a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Side 81 - If there be 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. Let...
Side 107 - IN obtuse angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle.
Side 96 - AB2+CK=2AB.BC-fHF, that is, (since CK=CB2, and HF=AC2,) AB2+CB2=2AB.BC+AC2. " COR. Hence, the sum of the squares of any two lines is equal to " twice the rectangle contained by the lines together with the square of