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, The Book of Euclid's Data, in Like Manner Corrected. viz. The first six books, together with the eleventh and twelfthA. Foulis, 1781 - 466 páginas |
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Página 8
... greater of two given fstraight lines to cut off a part equal to the less . Let AB and C be the two gi- ven straight lines , whereof AB is the greater . It is required to cut D A off from AB , the greater , a part C A equal to C the less ...
... greater of two given fstraight lines to cut off a part equal to the less . Let AB and C be the two gi- ven straight lines , whereof AB is the greater . It is required to cut D A off from AB , the greater , a part C A equal to C the less ...
Página 11
... greater than the other . let AB be the greater , and from it cut off DB equal to AC , the lefs , and join DC . therefore because in a . 3. 1 . the triangles DBC , ACB , DB is equal to A AC , and BC common to both , the two D 1 i fides ...
... greater than the other . let AB be the greater , and from it cut off DB equal to AC , the lefs , and join DC . therefore because in a . 3. 1 . the triangles DBC , ACB , DB is equal to A AC , and BC common to both , the two D 1 i fides ...
Página 12
... greater than the angle BCD , wherefore the angle FDC is likewife greater than BCD ; much C D more then is the angle BDC greater than B the angle BCD . again , because CB is e- qual to DB , the angle BDC is equal to the angle BCD ...
... greater than the angle BCD , wherefore the angle FDC is likewife greater than BCD ; much C D more then is the angle BDC greater than B the angle BCD . again , because CB is e- qual to DB , the angle BDC is equal to the angle BCD ...
Página 18
... greater than the angle ECF , there- fore the angle ACD is greater than BAE . in the fame manner , if the fide EC be bisected , it may be demonstrated that the angle BCG , that is , the angle ACD , is greater than the angle ABC ...
... greater than the angle ECF , there- fore the angle ACD is greater than BAE . in the fame manner , if the fide EC be bisected , it may be demonstrated that the angle BCG , that is , the angle ACD , is greater than the angle ABC ...
Página 19
... greater than the angles ABC , ACB . but ACD , ACB are together equal to two right angles ; therefore the angles ABC ... greater fide of every triangle greater angle . T is opposite to the Let ABC be a triangle of A which the fide ...
... greater than the angles ABC , ACB . but ACD , ACB are together equal to two right angles ; therefore the angles ABC ... greater fide of every triangle greater angle . T is opposite to the Let ABC be a triangle of A which the fide ...
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Términos y frases comunes
AC is equal alfo alſo angle ABC angle BAC bafe baſe BC is given becauſe the angle biſected Book XI cafe cauſe circle ABCD circumference cone conſtruction cylinder demonftrated deſcribed diameter drawn EFGH equal angles equiangular equimultiples Euclid exceſs faid fame multiple fame ratio fame reaſon fegment 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 line BC oppoſite parallel parallelepipeds parallelogram paſs perpendicular proportionals Propoſition pyramid Q. E. D. PROP rectangle contained rectilineal figure right angles ſame ſecond ſhall ſhall be equal ſhewn ſide ſpace ſphere ſquare of AC ſtraight line AC THEOR theſe thoſe thro tiple triangle ABC vertex wherefore
Pasajes populares
Página 156 - 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.
Página 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.
Página 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 92 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square- of the line which meets it, the line which meets shall touch the circle.
Página 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.
Página 52 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Página 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Página 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.
Página 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...