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, to this Second Edition is Added the Book of Euclid's Data. In Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthR. and A. Foulis, 1762 - 466 σελίδες |
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Αποτελέσματα 1 - 5 από τα 28.
Σελίδα 40
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a fquare upon AB ... BC , is equal to the fquares de- fcribed upon BA , AC . a On BC defcribe the fquare BDEC , and on BA , AC the squares ...
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a fquare upon AB ... BC , is equal to the fquares de- fcribed upon BA , AC . a On BC defcribe the fquare BDEC , and on BA , AC the squares ...
Σελίδα 41
... square HC . Therefore the whole fquare BDEC is equal to the two fquares GB , HC . and the fquare BDEC is described upon the straight line BC , and the fquares GB , HC upon BA , AC . wherefore the fquare upon the fide BC is equal to the ...
... square HC . Therefore the whole fquare BDEC is equal to the two fquares GB , HC . and the fquare BDEC is described upon the straight line BC , and the fquares GB , HC upon BA , AC . wherefore the fquare upon the fide BC is equal to the ...
Σελίδα 42
... BC one of the fides of the triangl ABC be equal to the fquares upon the other fides BA , AC ; the angle BAC is a ... square of DA is equal to the fquare of AB ; to each of these add the square of AC , therefore the fquares of DA , AC are ...
... BC one of the fides of the triangl ABC be equal to the fquares upon the other fides BA , AC ; the angle BAC is a ... square of DA is equal to the fquare of AB ; to each of these add the square of AC , therefore the fquares of DA , AC are ...
Σελίδα 46
... square ADEB , and join BD , and thro C draw b CGF parallel to AD or BE , and thro'G draw HK parallel to AB or DE ... BC is equal to the f . 34. 1. fide CG . but CB is equal also f to GK , and CG to BK ; wherefore the figure CGKB is ...
... square ADEB , and join BD , and thro C draw b CGF parallel to AD or BE , and thro'G draw HK parallel to AB or DE ... BC is equal to the f . 34. 1. fide CG . but CB is equal also f to GK , and CG to BK ; wherefore the figure CGKB is ...
Σελίδα 48
... square of CB , is equal to the fquare of CD . Upon CD describe the fquare CEFD , join DE , and thro ' B b . 31. 1 ... BC are point 48 THE ELEMENTS Book II. ...
... square of CB , is equal to the fquare of CD . Upon CD describe the fquare CEFD , join DE , and thro ' B b . 31. 1 ... BC are point 48 THE ELEMENTS Book II. ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe circle ABCD circumference cone confequently conftruction cylinder defcribed demonftrated drawn equal angles equiangular equimultiples Euclid excefs faid fame multiple fame ratio fame reaſon fecond fegment fhall fhewn fides fimilar firft firſt folid angle fome fore fquare of BC given angle given in fpecies given in magnitude given in pofition given magnitude given ratio given ſtraight line gnomon greater join lefs leſs Let ABC likewife line BC muſt oppofite parallel parallelepipeds parallelogram perpendicular polygon prifms Propofition proportionals pyramid Q. E. D. PROP reafon rectangle rectangle contained rectilineal figure right angles ſhall ſphere ſquare ſtraight line AB thefe THEOR theſe thro tiple triangle ABC wherefore
Δημοφιλή αποσπάσματα
Σελίδα 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 163 - 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 48 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 73 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle; and no straight line can be drawn from the extremity between that straight line and the circumference, so as not to cut the circle...
Σελίδα 105 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
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 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
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 47 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Σελίδα 37 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.