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 293
... yet it is science which must give the reason why two sides of a triangle are
greater than the third . but the right answer to ... is , that the number of Axioms
ought not to be encreased without necessity , as it must be if these Propositions
be not ...
... yet it is science which must give the reason why two sides of a triangle are
greater than the third . but the right answer to ... is , that the number of Axioms
ought not to be encreased without necessity , as it must be if these Propositions
be not ...
Σελίδα 294
Book I. that these circles must meet one another , because FD and GH are
together greater than FG ? and this determination is easier to be understood than
that which Mr. Thomas Simpson derives from it , and puts instead of Euclid's , in
the ...
Book I. that these circles must meet one another , because FD and GH are
together greater than FG ? and this determination is easier to be understood than
that which Mr. Thomas Simpson derives from it , and puts instead of Euclid's , in
the ...
Σελίδα 300
... for this is the thing to be demonstrated ; it is manifest some other point must be
affumed as the center ; and if from this assumption an absurdity follows , as
Euclid demonstrates there must ; then it is not true that the point assumed is the
center ...
... for this is the thing to be demonstrated ; it is manifest some other point must be
affumed as the center ; and if from this assumption an absurdity follows , as
Euclid demonstrates there must ; then it is not true that the point assumed is the
center ...
Σελίδα 327
To apply a rectangle which shall be equal to a given square , to a given straight
line , deficient by a square . but the given square must not be greater than that
upon the half of the given line . Let AB be the given straight line , and let the
square ...
To apply a rectangle which shall be equal to a given square , to a given straight
line , deficient by a square . but the given square must not be greater than that
upon the half of the given line . Let AB be the given straight line , and let the
square ...
Σελίδα 423
... because the perpendicular must be greater or less than LM or NO . but , as has
been shewn in the preceding demonstration , a triangle similar to ABC can be
defcribed in the fegment EGF upon the base EF , and the ratio of its
perpendicular ...
... because the perpendicular must be greater or less than LM or NO . but , as has
been shewn in the preceding demonstration , a triangle similar to ABC can be
defcribed in the fegment EGF upon the base EF , and the ratio of its
perpendicular ...
Τι λένε οι χρήστες - Σύνταξη κριτικής
Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
Άλλες εκδόσεις - Προβολή όλων
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 |