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 twelfth |
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Σελίδα 62
... the circumference . it falls therefore within it . Wherefore if any two points , & c .
Q. E. D. IF equal PROP . III . THEO R. F a straight line drawn thro ' the center of a
circle , bisect a straight line in it which does not pass thro ' the center , it shall ...
... the circumference . it falls therefore within it . Wherefore if any two points , & c .
Q. E. D. IF equal PROP . III . THEO R. F a straight line drawn thro ' the center of a
circle , bisect a straight line in it which does not pass thro ' the center , it shall ...
Σελίδα 63
IF in a Fin a circle two straight lines cut one another which do not both pass thro '
the center , they do not bifect each the other . Let ABCD be a circle , and AC , BD
two straight lines in it which cut one another in the point E , and do not both pass
...
IF in a Fin a circle two straight lines cut one another which do not both pass thro '
the center , they do not bifect each the other . Let ABCD be a circle , and AC , BD
two straight lines in it which cut one another in the point E , and do not both pass
...
Σελίδα 66
F any point be taken without a circle , and straight lines be drawn from it to the
circumference , whereof one passes thro ' the center ; of those which fall upon the
concave circumference the greatest is that which passes thro ' the center ; and of
...
F any point be taken without a circle , and straight lines be drawn from it to the
circumference , whereof one passes thro ' the center ; of those which fall upon the
concave circumference the greatest is that which passes thro ' the center ; and of
...
Σελίδα 89
A If AC , BD pass each of them through E so that E is the center ; it is evident , that
AE , EC , BE , ED , being all equal , the rectangle AE , EC is likewise equal to the
rectangle BE , ED . But let one of them BD pass thro ' the center , and cut the ...
A If AC , BD pass each of them through E so that E is the center ; it is evident , that
AE , EC , BE , ED , being all equal , the rectangle AE , EC is likewise equal to the
rectangle BE , ED . But let one of them BD pass thro ' the center , and cut the ...
Σελίδα 91
Either DCA passes thro ' the center , or it does not ; first , let it pass thro ' the
center E , and join EB ; D therefore the angle EBD is a right * angle . , and
because the straight line a . 18. 3 . AC is bifected in E , and produced to the point
D , the ...
Either DCA passes thro ' the center , or it does not ; first , let it pass thro ' the
center E , and join EB ; D therefore the angle EBD is a right * angle . , and
because the straight line a . 18. 3 . AC is bifected in E , and produced to the point
D , the ...
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Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
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Συχνά εμφανιζόμενοι όροι και φράσεις
added alſo altitude angle ABC angle BAC baſe becauſe Book caſe circle circle ABCD circumference common cone cylinder Definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs fame fides figure firſt folid angle fore four fourth given angle given in poſition given magnitude given ratio given ſtraight line greater half join leſs likewiſe magnitude manner meet multiple muſt oppoſite parallel parallelogram perpendicular plane produced PROP proportionals Propoſition pyramid radius reaſon rectangle rectangle contained rectilineal remaining right angles ſame ſecond ſegment ſhall ſides ſimilar ſolid ſphere ſquare ſquare of AC taken THEOR theſe third thro triangle ABC wherefore whole
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...
Πληροφορίες βιβλιογραφίας
| Τίτλος | 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 twelfth |
| Συγγραφέας | Robert Simson |
| Εκδότης | A. Foulis, 1781 |
| Πρωτότυπο από | το Πανεπιστήμιο του Μίτσιγκαν |
| Ψηφιοποιήθηκε στις | 11 Ιουν. 2007 |
| Μέγεθος | 466 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |