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 7
... equal ' to AB . and because the point B is the center of the circle ACE , c . 15th De- BC is equal to BA . but it has been proved that CA is equal to finition . AB ; therefore CA , CB are each of them equal to AB . but things which are ...
... equal ' to AB . and because the point B is the center of the circle ACE , c . 15th De- BC is equal to BA . but it has been proved that CA is equal to finition . AB ; therefore CA , CB are each of them equal to AB . but things which are ...
Seite 8
... equal to BG . and things that are equal to the same are equal to one another ; there- fore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC ...
... equal to BG . and things that are equal to the same are equal to one another ; there- fore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC ...
Seite 9
... equal to the angle EDF . the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal fides are opposite , shall be equal , each to each , viz . the angle ABC to the B ...
... equal to the angle EDF . the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal fides are opposite , shall be equal , each to each , viz . the angle ABC to the B ...
Seite 12
... equal to AD in the triangle E F 2. 5. 1 . ACD , the angles ECD , FDC upon the o- ther side of the base CD are equal ... BC equal to the base EF . The angle BAC is e- qual to the angle EDF . For if the tri- angle ABC be ap- B CE F ...
... equal to AD in the triangle E F 2. 5. 1 . ACD , the angles ECD , FDC upon the o- ther side of the base CD are equal ... BC equal to the base EF . The angle BAC is e- qual to the angle EDF . For if the tri- angle ABC be ap- B CE F ...
Seite 13
... equal to one another , and likewife their fides terminated in the other extremity . but this is im- possible . therefore if the base BC coincides with the base EF , the a . 7. 1 . fides BA , AC cannot but coincide with the fides ED , DF ...
... equal to one another , and likewife their fides terminated in the other extremity . but this is im- possible . therefore if the base BC coincides with the base EF , the a . 7. 1 . fides BA , AC cannot but coincide with the fides ED , DF ...
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alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio biſected Book XI cafe cauſe circle ABCD circumference cone conſtruction cylinder demonftrated deſcribed diameter drawn equal angles equiangular equimultiples Euclid exceſs fame multiple fame ratio fame reaſon fides fimilar firſt folid angle fore given angle given in magnitude given in poſition given in ſpecies given magnitude given ratio given ſtraight line gnomon greater join leſs Let ABC likewife oppoſite parallel parallelepipeds parallelogram perpendicular priſms Propofition proportionals pyramid Q. E. D. PROP rectangle rectangle contained rectilineal figure right angles ſame ſecond ſegment ſhall ſhewn ſide ſpace ſphere ſquare of AC ſtraight line AB ſtraight line BC THEOR theſe thoſe tiple triangle ABC vertex 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.