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 σελίδες |
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Σελίδα
... 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 ...
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 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 ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...