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, The Book of Euclid's Data, in Like Manner Corrected. viz. The first six books, together with the eleventh and twelfthA. Foulis, 1781 - 466 sider |
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Resultat 1-5 av 53
Side 111
... fourth , when any equimultiples whatsoever of the firft and third being taken , and any equimul- tiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the fecond , the multiple of the third is ...
... fourth , when any equimultiples whatsoever of the firft and third being taken , and any equimul- tiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the fecond , the multiple of the third is ...
Side 112
... fourth . VI . Magnitudes which have the fame ratio are called proportionals . N. B. When four magnitudes are proportionals , it is ufually expreffed by saying , the firft is to the fecond , as the third to ' the fourth . ' VII . When of ...
... fourth . VI . Magnitudes which have the fame ratio are called proportionals . N. B. When four magnitudes are proportionals , it is ufually expreffed by saying , the firft is to the fecond , as the third to ' the fourth . ' VII . When of ...
Side 113
... fourth ; or that the first is to the third , as the fecond to the fourth . as is fhewn in the 16th Prop . of this 5th Book . XIV . Invertendo , by Inverfion ; when there are four proportionals , and it is inferred , that the fecond is ...
... fourth ; or that the first is to the third , as the fecond to the fourth . as is fhewn in the 16th Prop . of this 5th Book . XIV . Invertendo , by Inverfion ; when there are four proportionals , and it is inferred , that the fecond is ...
Side 114
... fourth of the first rank , fo is the third from the last to the last but two of the fecond rank ; and fo on in a cross order . and the inference is as in the 18th Definition . It is demonftrated in 23d Prop . of Book 5th . A X I O M ...
... fourth of the first rank , fo is the third from the last to the last but two of the fecond rank ; and fo on in a cross order . and the inference is as in the 18th Definition . It is demonftrated in 23d Prop . of Book 5th . A X I O M ...
Side 116
... fourth , and the fifth the fame multiple of the fecond that the fixth is of the fourth ; then fhall the first together with the fifth be the fame multiple of the fecond , that the third toge- ther with the fixth is of the fourth . Let ...
... fourth , and the fifth the fame multiple of the fecond that the fixth is of the fourth ; then fhall the first together with the fifth be the fame multiple of the fecond , that the third toge- ther with the fixth is of the fourth . Let ...
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 Ago ... Robert Simson Uten tilgangsbegrensning - 1762 |
The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... Robert Simson Uten tilgangsbegrensning - 1827 |
Vanlige uttrykk og setninger
AC is equal alfo alſo angle ABC angle BAC bafe baſe BC is given becauſe the angle bifected Book XI cafe circle ABCD circumference cone confequently cylinder defcribed demonftrated diameter drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fecond fegment fhall fhewn fide BC fides fimilar fince firft firſt folid angle fome fore fquare of AC ftraight line AB given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs leſs likewife line BC muſt oppofite parallel parallelepipeds parallelogram perpendicular prifm Propofition proportionals pyramid rectangle contained rectilineal figure right angles ſhall ſphere ſquare thefe THEOR theſe thro tiple triangle ABC vertex wherefore
Populære avsnitt
Side 156 - 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 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 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 92 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square- of the line which meets it, the line which meets shall touch the circle.
Side 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.
Side 52 - 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 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
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 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...