The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, to this Second Edition is Added the Book of Euclid's Data. In Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthR. and A. Foulis, 1762 - 466 sider |
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Side 59
... DEFINITION S. I. QUAL circles are thofe of which the diameters are equal , or from the centers of which the straight lines to the circumfe- rences are equal . ' This is not a Definition but a Theorem , the truth of which is ' evident ...
... DEFINITION S. I. QUAL circles are thofe of which the diameters are equal , or from the centers of which the straight lines to the circumfe- rences are equal . ' This is not a Definition but a Theorem , the truth of which is ' evident ...
Side 111
... DEFINITIONS . I. " LESS magnitude is faid to be a part of a greater magnitude , when the lefs measures the greater , that is , when the lefs is ' contained a certain number of times exactly in the greater . ' II . A greater magnitude is ...
... DEFINITIONS . I. " LESS magnitude is faid to be a part of a greater magnitude , when the lefs measures the greater , that is , when the lefs is ' contained a certain number of times exactly in the greater . ' II . A greater magnitude is ...
Side 112
... Definition ) the multiple of the first is greater than that of the fe- cond , but the multiple of the third is not greater than the mul- tiple of the fourth ; then the firft is faid to have to the fecond a greater ratio than the third ...
... Definition ) the multiple of the first is greater than that of the fe- cond , but the multiple of the third is not greater than the mul- tiple of the fourth ; then the firft is faid to have to the fecond a greater ratio than the third ...
Side 113
... Definition , A is faid to have to D the ra- Book V. tio compounded of ratios which are the fame with the ratios of E to F , G to H , and K to L. and the fame thing is to be under- ftood when it is more briefly expreffed by saying A has ...
... Definition , A is faid to have to D the ra- Book V. tio compounded of ratios which are the fame with the ratios of E to F , G to H , and K to L. and the fame thing is to be under- ftood when it is more briefly expreffed by saying A has ...
Side 114
... Definition ; whence this is called Ordinate Proportion . It is demonftrated in 22d Prop . Book 5th . XX . Ex aequali , in proportione perturbata , feu inordinata , from equa- lity , in perturbate or diforderly proportion * ; this term ...
... Definition ; whence this is called Ordinate Proportion . It is demonftrated in 22d Prop . Book 5th . XX . Ex aequali , in proportione perturbata , feu inordinata , from equa- lity , in perturbate or diforderly proportion * ; this term ...
Andre utgaver - Vis alle
The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ... Robert Simson Uten tilgangsbegrensning - 1775 |
The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... Robert Simson Uten tilgangsbegrensning - 1827 |
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1781 |
Vanlige uttrykk og setninger
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe circle ABCD circumference cone confequently conftruction cylinder defcribed demonftrated drawn equal angles equiangular equimultiples Euclid excefs faid fame multiple fame ratio fame reaſon fecond fegment fhall fhewn fides fimilar firft firſt folid angle fome fore fquare of BC given angle given in fpecies given in magnitude given in pofition given magnitude given ratio given ſtraight line gnomon greater join lefs leſs Let ABC likewife line BC muſt oppofite parallel parallelepipeds parallelogram perpendicular polygon prifms Propofition proportionals pyramid Q. E. D. PROP reafon rectangle rectangle contained rectilineal figure right angles ſhall ſphere ſquare ſtraight line AB thefe THEOR theſe thro tiple triangle ABC wherefore
Populære avsnitt
Side 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 163 - 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 48 - 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 73 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle; and no straight line can be drawn from the extremity between that straight line and the circumference, so as not to cut the circle...
Side 105 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Side 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Side 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Side 47 - 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 37 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.