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 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 77.
Σελίδα 9
... BAC equal to the angle EDF . the bafe BC fhall be e- equal to the bafe EF ; and the triangle ABC to the triangle DEF ; and the other angies , to which the equal fides are opposite , shall be equal , each to each , viz . the angle ABC ...
... BAC equal to the angle EDF . the bafe BC fhall be e- equal to the bafe EF ; and the triangle ABC to the triangle DEF ; and the other angies , to which the equal fides are opposite , shall be equal , each to each , viz . the angle ABC ...
Σελίδα 12
... angle ECD is greater than the angle BCD , wherefore the angle FDC is likewife greater than BCD ; much more then is ... BAC is equal to the angle EDF . For if the trian- gle ABC be applied D G to DEF fo that the B CE F point B be on E ...
... angle ECD is greater than the angle BCD , wherefore the angle FDC is likewife greater than BCD ; much more then is ... BAC is equal to the angle EDF . For if the trian- gle ABC be applied D G to DEF fo that the B CE F point B be on E ...
Σελίδα 13
... angle BAC coincides with the angle EDF , and is equal to it . therefore if two triangles , & c . Q. E. D. b . 8. Ax . PROP . IX . PROB . TO bifect a given rectilineal angle , that is , to divide it into two equal angles . a b . 1. 1 ...
... angle BAC coincides with the angle EDF , and is equal to it . therefore if two triangles , & c . Q. E. D. b . 8. Ax . PROP . IX . PROB . TO bifect a given rectilineal angle , that is , to divide it into two equal angles . a b . 1. 1 ...
Σελίδα 18
... angle ACD is greater than either of the interior op posite angles CBA , BAC . A F 4 Bifect AC in E , join BE and ... angle AEB is B equal to the angle CEF , be- caufe they are oppofite verti- cal angles . therefore the bafe AB is equal ...
... angle ACD is greater than either of the interior op posite angles CBA , BAC . A F 4 Bifect AC in E , join BE and ... angle AEB is B equal to the angle CEF , be- caufe they are oppofite verti- cal angles . therefore the bafe AB is equal ...
Σελίδα 19
... BAC , ACB , as also CAB , ABC are less than two right an- gles . therefore any two angles , & c . Q. E. D. THE PROP . XVIII . THE OR . greater fide of every triangle is opposite to the greater angle . Let ABC be a triangle of which the ...
... BAC , ACB , as also CAB , ABC are less than two right an- gles . therefore any two angles , & c . Q. E. D. THE PROP . XVIII . THE OR . greater fide of every triangle is opposite to the greater angle . Let ABC be a triangle of which the ...
Άλλες εκδόσεις - Προβολή όλων
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...