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 8
... greater of off a part equal to the lefs . Let AB and C be the two gi- ven ftraight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part equal to C the lefs . From the point A draw the straight ...
... greater of off a part equal to the lefs . Let AB and C be the two gi- ven ftraight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part equal to C the lefs . From the point A draw the straight ...
Seite 11
... greater than the o- ther , let AB be the greater , and from it cut off DB equal to AC , the a . 1 . less , and join DC . therefore because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two fides DB , BC ...
... greater than the o- ther , let AB be the greater , and from it cut off DB equal to AC , the a . 1 . less , and join DC . therefore because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two fides DB , BC ...
Seite 12
... greater than BCD ; much more then is the angle BDC greater than D the angle BCD . again , because CB is e A B qual to DB , the angle BDC is equal to the angle BCD ; but BDC has been proved to be greater than the fame BCD , which is ...
... greater than BCD ; much more then is the angle BDC greater than D the angle BCD . again , because CB is e A B qual to DB , the angle BDC is equal to the angle BCD ; but BDC has been proved to be greater than the fame BCD , which is ...
Seite 18
... greater than the angle ECF , therefore the angle ACD is greater than BAE . in the fame man- ner , if the fide BC be bisected , it may be demonstrated that the angle BCG , that is , the angle ACD , is greater than the angle 4. 15. 1 ...
... greater than the angle ECF , therefore the angle ACD is greater than BAE . in the fame man- ner , if the fide BC be bisected , it may be demonstrated that the angle BCG , that is , the angle ACD , is greater than the angle 4. 15. 1 ...
Seite 19
... greater fide of every triangle is opposite greater angle . Let ABC be a triangle of which the fide AC is greater than the side AB ; the angle ABC is also greater than the angle BCA . B A tổ thế D 2. 3. 1 , C Because AC is greater ...
... greater fide of every triangle is opposite greater angle . Let ABC be a triangle of which the fide AC is greater than the side AB ; the angle ABC is also greater than the angle BCA . B A tổ thế D 2. 3. 1 , C Because AC is greater ...
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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.