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 248
Book XII . is to the space S. therefore as the circle ABCD is to the space S , fe is
the polygon AXBOCPDR to the polygon EKFLGMHN . but the circle ABCD is
greater than the polygon contained in it ; wherefore the space S is greater d than
the ...
Book XII . is to the space S. therefore as the circle ABCD is to the space S , fe is
the polygon AXBOCPDR to the polygon EKFLGMHN . but the circle ABCD is
greater than the polygon contained in it ; wherefore the space S is greater d than
the ...
Σελίδα 249
the square of BD , so is the circle EFGH to a space less than the Book XII . circle
ABCD , which has been demonstrated to be impoflible . therefore the square of
BD is not to the square of FH , as the circle ABCD is to any space greater than the
...
the square of BD , so is the circle EFGH to a space less than the Book XII . circle
ABCD , which has been demonstrated to be impoflible . therefore the square of
BD is not to the square of FH , as the circle ABCD is to any space greater than the
...
Σελίδα 266
Book xır : GR , RH , HS , SE . therefore the remainder of the cone , viz . the
pyramid of which the base is the polygon EOFPGRHS , and its vertex the fame
with that of the cone , is greater than the folid X. In the circle ABCD describe the
polygon ...
Book xır : GR , RH , HS , SE . therefore the remainder of the cone , viz . the
pyramid of which the base is the polygon EOFPGRHS , and its vertex the fame
with that of the cone , is greater than the folid X. In the circle ABCD describe the
polygon ...
Σελίδα 267
not to the circle EFGH , as the cone AL to any folid which is less Book XII . than
the cone EN . In the fame manner may be demonstrated that the circle EFGH is
not to the circle ABCD , as the cone EN to any folid less than the cone AL . Nor
can ...
not to the circle EFGH , as the cone AL to any folid which is less Book XII . than
the cone EN . In the fame manner may be demonstrated that the circle EFGH is
not to the circle ABCD , as the cone EN to any folid less than the cone AL . Nor
can ...
Σελίδα 275
EO is cut by the plane TYS parallel to its opposite planes . there- Book XII . fore
as the base ABCD to the base EFGH ... EFGH be two given circles having the
same center K. it is required to inscribe in the greater circle ABCD a polygon of
an ...
EO is cut by the plane TYS parallel to its opposite planes . there- Book XII . fore
as the base ABCD to the base EFGH ... EFGH be two given circles having the
same center K. it is required to inscribe in the greater circle ABCD a polygon of
an ...
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 |