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 68
Side
... must be demonftrated , and not affumed . and therefore , tho ' this were a true Propofition , it ought to have been demonftrated . But indeed this Propofition , which makes the 10th Definition of the 11th Book , is not true univerfally ...
... must be demonftrated , and not affumed . and therefore , tho ' this were a true Propofition , it ought to have been demonftrated . But indeed this Propofition , which makes the 10th Definition of the 11th Book , is not true univerfally ...
Side 21
... must be greater than the third " . Let A , B , C be the three given straight lines , of which any two whatever are greater than the third , viz . A and B greater than C ; A and C greater than B ; and B and C than A. It is required to ...
... must be greater than the third " . Let A , B , C be the three given straight lines , of which any two whatever are greater than the third , viz . A and B greater than C ; A and C greater than B ; and B and C than A. It is required to ...
Side 24
... must either be equal to it , or less . but the angle BAC is not equal to the angle EDF , because them the bafe BC would be a equal to EF . but it is not ; therefore the angle BAC is not e- qual to the angle EDF . neither is it lefs ; be ...
... must either be equal to it , or less . but the angle BAC is not equal to the angle EDF , because them the bafe BC would be a equal to EF . but it is not ; therefore the angle BAC is not e- qual to the angle EDF . neither is it lefs ; be ...
Side 27
... must be greater than the- E A B H D F other ; let AGH be the greater . and be - C cause the angle AGH is greater than the angle GHD , add to each of them a the angle BGH ; therefore the angles AGH , BGH are greater than the angles BGH ...
... must be greater than the- E A B H D F other ; let AGH be the greater . and be - C cause the angle AGH is greater than the angle GHD , add to each of them a the angle BGH ; therefore the angles AGH , BGH are greater than the angles BGH ...
Side 69
... must pass thro ' it . Therefore if two circles , & c . Q. E. D. IF PROP . XII . THE OR . 2. 20. I. two circles touch each other externally , the ftraight line which joins their centers fhall pass thro ' the point of contact . Let the ...
... must pass thro ' it . Therefore if two circles , & c . Q. E. D. IF PROP . XII . THE OR . 2. 20. I. two circles touch each other externally , the ftraight line which joins their centers fhall pass thro ' the point of contact . Let the ...
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...