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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Σελίδα
... taken for granted , that thofe folid angles are equal to one ano- ther which are contained by plane angles of the fame number and magnitude placed in the fame order ; but neither is this universally true , except in the cafe in which ...
... taken for granted , that thofe folid angles are equal to one ano- ther which are contained by plane angles of the fame number and magnitude placed in the fame order ; but neither is this universally true , except in the cafe in which ...
Σελίδα 1
... taken , See N. the straight line between them lies wholly in that fuperficies . VIII . " A plane angle is the inclination of two lines to one another in a See N. 66 plane , which meet together , but are not in the fame direction . " IX ...
... taken , See N. the straight line between them lies wholly in that fuperficies . VIII . " A plane angle is the inclination of two lines to one another in a See N. 66 plane , which meet together , but are not in the fame direction . " IX ...
Σελίδα 5
... taken from equals , the remainders are equal . IV . If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remainders are unequal . VI . Things which are double of the fame , are equal to one ...
... taken from equals , the remainders are equal . IV . If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remainders are unequal . VI . Things which are double of the fame , are equal to one ...
Σελίδα 6
... taken together 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 ...
... taken together 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 ...
Σελίδα 61
... taken in the circumference of a circle , the straight line which joins them shall fall within the circle . Let ABC be a circle , and A , B any two points in the circum- ference ; the ftraight line drawn from A to B fhall fall within the ...
... taken in the circumference of a circle , the straight line which joins them shall fall within the circle . Let ABC be a circle , and A , B any two points in the circum- ference ; the ftraight line drawn from A to B fhall fall within the ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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...