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 278
Sr N. To describe in the greater of two spheres which have the same center , a
solid polyhedron , the superficies of which shall not meet the lesser sphere . Let
there be two spheres about the fame center A ; it is required to describe in the ...
Sr N. To describe in the greater of two spheres which have the same center , a
solid polyhedron , the superficies of which shall not meet the lesser sphere . Let
there be two spheres about the fame center A ; it is required to describe in the ...
Σελίδα 283
And if in the lesser sphere there be described a solid polyhedron by drawing
straight lines betwixt the points in which the Straight lines from the center of the
sphere drawn to all the angles of the folid polyhedron in the greater sphere meet
the ...
And if in the lesser sphere there be described a solid polyhedron by drawing
straight lines betwixt the points in which the Straight lines from the center of the
sphere drawn to all the angles of the folid polyhedron in the greater sphere meet
the ...
Σελίδα 284
Wherefore the whole solid polyhedron in the greater sphere has to the whole
tolid polyhedron in the other , the triplicate ratio of that ... THEOR , SPHERES
PHERES have to one another the triplicate ratio of that which their diameters
have .
Wherefore the whole solid polyhedron in the greater sphere has to the whole
tolid polyhedron in the other , the triplicate ratio of that ... THEOR , SPHERES
PHERES have to one another the triplicate ratio of that which their diameters
have .
Σελίδα 285
therefore • also the sphere GHK is greater than the folid polyhe - Book XII . dron
in the sphere DEF . but it is also less , because it is contained within it , which is
imposible . therefore the sphere ABC has not to c . 14 S. any sphere less than
DEF ...
therefore • also the sphere GHK is greater than the folid polyhe - Book XII . dron
in the sphere DEF . but it is also less , because it is contained within it , which is
imposible . therefore the sphere ABC has not to c . 14 S. any sphere less than
DEF ...
Σελίδα 13
DEFINITION S. TH I. THE pole of a circle of the sphere is a point in the fuperficies
of the sphere , from which all straight lines drawn to the circumference of the
circle are equal . II . A great circle of the sphere is any whose plane passes
through ...
DEFINITION S. TH I. THE pole of a circle of the sphere is a point in the fuperficies
of the sphere , from which all straight lines drawn to the circumference of the
circle are equal . II . A great circle of the sphere is any whose plane passes
through ...
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 |