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 Seiten |
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Seite 10
... join FC , GB . A Because AF is equal to AG , and AB to AC ; the two fides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG common to the two tri- angles AFC , AGB ; therefore the base FC is equal to ...
... join FC , GB . A Because AF is equal to AG , and AB to AC ; the two fides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG common to the two tri- angles AFC , AGB ; therefore the base FC is equal to ...
Seite 11
... join DC . therefore because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two fides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; therefore the base DC ...
... join DC . therefore because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two fides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; therefore the base DC ...
Seite 13
... join DE , and upon it defcribeban equilateral triangle DEF , then join AF . the straight line AF bifects the angle BAC . Because AD is equal to AE , and AF is common to the two triangles DAF , EAF ; the two fides DA , AF are equal to ...
... join DE , and upon it defcribeban equilateral triangle DEF , then join AF . the straight line AF bifects the angle BAC . Because AD is equal to AE , and AF is common to the two triangles DAF , EAF ; the two fides DA , AF are equal to ...
Seite 14
... join FC . the ftraight line FC drawn from the given point C , is at right angles to the given straight line AB . F Becaufe DC is equal to CE , and FC common to the two tri- A D C angles DCF , ECF ; the two fides EB c . 8. I. d . 10. Def ...
... join FC . the ftraight line FC drawn from the given point C , is at right angles to the given straight line AB . F Becaufe DC is equal to CE , and FC common to the two tri- A D C angles DCF , ECF ; the two fides EB c . 8. I. d . 10. Def ...
Seite 18
... join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. b B A E Ꭰ G Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is equal to the angle ...
... join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. b B A E Ꭰ G Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is equal to the angle ...
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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
Beliebte Passagen
Seite 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 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.
Seite 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.
Seite 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...
Seite 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...
Seite 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.
Seite 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Seite 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.
Seite 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.
Seite 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.