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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Αποτελέσματα 1 - 5 από τα 6.
Σελίδα 262
Book XII . greater than the half of the circle ABCD + . upon the square ABCD
ereét a prikin of the fame altitude with the cylinder ; this priim is greater than half
of the cylinder ; because if a square be defcribed about the circle , and a piiiin
crected ...
Book XII . greater than the half of the circle ABCD + . upon the square ABCD
ereét a prikin of the fame altitude with the cylinder ; this priim is greater than half
of the cylinder ; because if a square be defcribed about the circle , and a piiiin
crected ...
Σελίδα 437
... wherefore the rectangle BC , CD is to the square of BD , as ( the square of KG
the half of MG to the square of GL , that is as ) the square of AB to the square of
BD , because as LG to GK , so DB was made to BA . therefore b the rectangle BC
...
... wherefore the rectangle BC , CD is to the square of BD , as ( the square of KG
the half of MG to the square of GL , that is as ) the square of AB to the square of
BD , because as LG to GK , so DB was made to BA . therefore b the rectangle BC
...
Σελίδα 5
IN N a plain triangle , the sum of any two sides is to their difference , as the
tangent of half the sum of the angles at the base , to the tangent of half their
difference . Let ABC be a plain triangle , the sum of any two fides AB , AC will be
to their ...
IN N a plain triangle , the sum of any two sides is to their difference , as the
tangent of half the sum of the angles at the base , to the tangent of half their
difference . Let ABC be a plain triangle , the sum of any two fides AB , AC will be
to their ...
Σελίδα 9
Half the given sum added 10 half the given difference , will be the greater , and
half the difference subtracted from half the sum , will be the lefs . For , let AB be
the given fum , AC the greater , and BC the less . Let AD be half the given fuin ;
and ...
Half the given sum added 10 half the given difference , will be the greater , and
half the difference subtracted from half the sum , will be the lefs . For , let AB be
the given fum , AC the greater , and BC the less . Let AD be half the given fuin ;
and ...
Σελίδα 34
THE rectangle contained by half of the radius , and ' HE the excess of the versed
lines of two arches , is equal to the rectangle contained by the fines of half the
fum , and half the difference of the fame arches , Let AB , AC be any two arches ...
THE rectangle contained by half of the radius , and ' HE the excess of the versed
lines of two arches , is equal to the rectangle contained by the fines of half the
fum , and half the difference of the fame arches , Let AB , AC be any two arches ...
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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 |