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 sider |
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Resultat 6-10 av 14
Side 56
... opposite angle , and the acute angle . a Let ABC be any triangle , and the angle at B one of its acute angles , and upon BC one of the fides containing it let fall the perpen . 3. 12. 1. dicular AD from the oppofite angle . the fquare ...
... opposite angle , and the acute angle . a Let ABC be any triangle , and the angle at B one of its acute angles , and upon BC one of the fides containing it let fall the perpen . 3. 12. 1. dicular AD from the oppofite angle . the fquare ...
Side 63
... opposite to one of the equal angles in each , is common to both ; therefore the other fides are equal , AF therefore is equal to FB . Wherefore if a straight line , & c . Q. E. D. I not PROP . IV . THEOR . [ F in a circle two straight ...
... opposite to one of the equal angles in each , is common to both ; therefore the other fides are equal , AF therefore is equal to FB . Wherefore if a straight line , & c . Q. E. D. I not PROP . IV . THEOR . [ F in a circle two straight ...
Side 99
... opposite to the right angle ; and if it be an obtufe . angled triangle , the center falls Without the triangle , beyond the fide oppofite to the obtufe angle . PROP . VI . PROB . To inscribe a square in a given circle . Let ABCD be the ...
... opposite to the right angle ; and if it be an obtufe . angled triangle , the center falls Without the triangle , beyond the fide oppofite to the obtufe angle . PROP . VI . PROB . To inscribe a square in a given circle . Let ABCD be the ...
Side 153
... opposite to the equal angles . F A B c . 12. Ax . 1 . d . 28. 1 . C E Let the triangle DCE be placed fo that its fide CE may be con- tiguous to BC , and in the fame straight line with it . and because the angles ABC , ACB are together ...
... opposite to the equal angles . F A B c . 12. Ax . 1 . d . 28. 1 . C E Let the triangle DCE be placed fo that its fide CE may be con- tiguous to BC , and in the fame straight line with it . and because the angles ABC , ACB are together ...
Side 154
... opposite to the homologous fides , viz . the angle ABC equal to the angle DEF , and BCA to EFD , and alfo BAC to EDF . a At the points E , F in the straight line EF make the angle FEG equal to the angle ABC , and the angle EFG equal to ...
... opposite to the homologous fides , viz . the angle ABC equal to the angle DEF , and BCA to EFD , and alfo BAC to EDF . a At the points E , F in the straight line EF make the angle FEG equal to the angle ABC , and the angle EFG equal to ...
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 ... Robert Simson Uten tilgangsbegrensning - 1827 |
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1781 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 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.
Side 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.
Side 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...
Side 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...
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 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
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 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.
Side 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.