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 44
Let A and BC be two straight lines ; and let BC be divided into any parts in the
points D , E ; the rectangle contained by the straight lines A , BC is equal to B В
D E C С the rectangle contained by A , BD ; and to that contained by A , DE ; and
...
Let A and BC be two straight lines ; and let BC be divided into any parts in the
points D , E ; the rectangle contained by the straight lines A , BC is equal to B В
D E C С the rectangle contained by A , BD ; and to that contained by A , DE ; and
...
Σελίδα 45
is the rectangle contained by BA , AC ; for it is contained by Book II . DA , AC , of
which AD is equal to AB ; and CE is contained by AB , BC , for BE is equal to AB .
therefore the rectangle contained by AB , AC together with the rectangle AB , BC
...
is the rectangle contained by BA , AC ; for it is contained by Book II . DA , AC , of
which AD is equal to AB ; and CE is contained by AB , BC , for BE is equal to AB .
therefore the rectangle contained by AB , AC together with the rectangle AB , BC
...
Σελίδα 164
F four straight lines be proportionals , the rectangle contained by the extremes is
equal to the rectangle contained by the means , and if the rectangle contained by
the extremes be equal to the rectangle contained by the means , the four ...
F four straight lines be proportionals , the rectangle contained by the extremes is
equal to the rectangle contained by the means , and if the rectangle contained by
the extremes be equal to the rectangle contained by the means , the four ...
Σελίδα 165
IF F three straight lines be proportionals , the rectangle contained by the
extremes is equal to the square of the mean . and if the rectangle contained by
the extremes be equal to the square of the mean , the three straight lines are
proportionals ...
IF F three straight lines be proportionals , the rectangle contained by the
extremes is equal to the square of the mean . and if the rectangle contained by
the extremes be equal to the square of the mean , the three straight lines are
proportionals ...
Σελίδα 35
25 , IN N a spherical triangle , the rectangle contained by the lines of the two
sides , is to the square of the radius , as the rectangle contained by the line of the
arch which is half the sum of the base , and the excess of the sides , and the line
of ...
25 , IN N a spherical triangle , the rectangle contained by the lines of the two
sides , is to the square of the radius , as the rectangle contained by the line of the
arch which is half the sum of the base , and the excess of the sides , and the line
of ...
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 |