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 60
... circle is the figure con- tained by two straight lines drawn from the center , and the circumfe- rence between them . XI . Similar fegments of a circle , are those in which the an- gles are equal , or which contain equal angles . PROP ...
... circle is the figure con- tained by two straight lines drawn from the center , and the circumfe- rence between them . XI . Similar fegments of a circle , are those in which the an- gles are equal , or which contain equal angles . PROP ...
Σελίδα 61
... circle ABC . Which was to be found . COR . From this it is manifeft , that if in a circle a straight line bifect another at right angles , the center of the circle is in the line which bifects the other . PROP . II . THEO R. IF any two ...
... circle ABC . Which was to be found . COR . From this it is manifeft , that if in a circle a straight line bifect another at right angles , the center of the circle is in the line which bifects the other . PROP . II . THEO R. IF any two ...
Σελίδα 62
... circle , bifect a ftraight line in it which does not pass thro ' the center , it shall cut it at right angles . and if it cuts it at right angles , it fhall bifect it . Let ABC be a circle ; and let CD a straight line drawn thro ' the ...
... circle , bifect a ftraight line in it which does not pass thro ' the center , it shall cut it at right angles . and if it cuts it at right angles , it fhall bifect it . Let ABC be a circle ; and let CD a straight line drawn thro ' the ...
Σελίδα 63
... circle two straight lines cut one another which do not both pass thro ' the center , they do not bi- fect each the other . Let ABCD be a circle , and AC , BD two ftraight lines in it which cut one another in the point E , and do not ...
... circle two straight lines cut one another which do not both pass thro ' the center , they do not bi- fect each the other . Let ABCD be a circle , and AC , BD two ftraight lines in it which cut one another in the point E , and do not ...
Σελίδα 64
... circle ABC , CF is equal to FB . alfo because F is the center of the circle CDE , CF is equal to FE . and CF was fhewn equal to FB ; therefore A FE is equal to FB , the lefs to the greater , which is impoffible . where- fore F is not ...
... circle ABC , CF is equal to FB . alfo because F is the center of the circle CDE , CF is equal to FE . and CF was fhewn equal to FB ; therefore A FE is equal to FB , the lefs to the greater , which is impoffible . where- fore F is not ...
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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...