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 σελίδες |
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Αποτελέσματα 1 - 5 από τα 88.
Σελίδα 6
... less " than two right angles , thefe ftraight lines being continually " produced fhall at length meet upon that fide on which are " the angles which are lefs than two right angles . See the '66 notes on Prop . 29. of Book I ...
... less " than two right angles , thefe ftraight lines being continually " produced fhall at length meet upon that fide on which are " the angles which are lefs than two right angles . See the '66 notes on Prop . 29. of Book I ...
Σελίδα 10
... less , and join FC , GB . a 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 bafe FC ...
... less , and join FC , GB . a 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 bafe FC ...
Σελίδα 19
... less than two right an- gles . therefore any two angles , & c . Q. E. D. THE PROP . XVIII . THE OR . greater fide of every triangle is opposite to the greater angle . Let ABC be a triangle of which the fide AC is greater than the fide ...
... less than two right an- gles . therefore any two angles , & c . Q. E. D. THE PROP . XVIII . THE OR . greater fide of every triangle is opposite to the greater angle . Let ABC be a triangle of which the fide AC is greater than the fide ...
Σελίδα 20
... less than the other two fides of the triangle , but fhall contain a greater angle . Let the two ftraight lines BD , CD be drawn from B , C , the ends of the fide BC of the triangle ABC , to the point D within it . BD and DC are lefs ...
... less than the other two fides of the triangle , but fhall contain a greater angle . Let the two ftraight lines BD , CD be drawn from B , C , the ends of the fide BC of the triangle ABC , to the point D within it . BD and DC are lefs ...
Σελίδα 24
... less . but the angle BAC is not equal to the angle EDF , because them the bafe BC would be a equal to EF . but it is not ; therefore the angle BAC is not e- qual to the angle EDF . neither is it lefs ; be- cause then the base BC would ...
... less . but the angle BAC is not equal to the angle EDF , because them the bafe BC would be a equal to EF . but it is not ; therefore the angle BAC is not e- qual to the angle EDF . neither is it lefs ; be- cause then the base BC would ...
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AC is equal alfo alſo angle ABC angle BAC bafe baſe BC is given becauſe the angle bifected Book XI cafe circle ABCD circumference cone confequently cylinder defcribed demonftrated diameter drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fecond fegment fhall fhewn fide BC fides fimilar fince firft firſt folid angle fome fore fquare of AC ftraight line AB given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs leſs likewife line BC muſt oppofite parallel parallelepipeds parallelogram perpendicular prifm Propofition proportionals pyramid rectangle contained rectilineal figure right angles ſhall ſphere ſquare thefe THEOR theſe thro tiple triangle ABC vertex wherefore
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...