Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added Elements of Plane and Spherical Trigonometry |
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Σελίδα 108
... is contained a certain number of times , exactly , in the greater . II . A greater
magnitude is said to be a multiple of a less , when the greater is measured by the
less , that is , when the greater contains the less a certain number of times exactly
.
... is contained a certain number of times , exactly , in the greater . II . A greater
magnitude is said to be a multiple of a less , when the greater is measured by the
less , that is , when the greater contains the less a certain number of times exactly
.
Σελίδα 112
If any number of magnitudes be equimultiples of as many others , each of each ,
what multiple soever any one of the first is of its part , the same multiple is the
sum of all the first of the sum of all the rest . Let any number of magnitudes A , B ...
If any number of magnitudes be equimultiples of as many others , each of each ,
what multiple soever any one of the first is of its part , the same multiple is the
sum of all the first of the sum of all the rest . Let any number of magnitudes A , B ...
Σελίδα 113
For the same reason the multiples of nB and nD by q , are qnB , on D. Since ,
therefore , A : B :: C : D , and of A and C ... If one magnitude be the same multiple
of another , which a magnitude taken from the first is of a magnitude taken from
the ...
For the same reason the multiples of nB and nD by q , are qnB , on D. Since ,
therefore , A : B :: C : D , and of A and C ... If one magnitude be the same multiple
of another , which a magnitude taken from the first is of a magnitude taken from
the ...
Σελίδα 115
Next , Let C be the same part of A that D is of B ; then A is the same multiple of C
that B is of D , and therefore , as has been demonstrated , A : C :: B : D , and
inversely ( A. 5. ) C : A :: D : B. Therefore , & c . Q. E. D. PROP . C. THEOR . If the
first ...
Next , Let C be the same part of A that D is of B ; then A is the same multiple of C
that B is of D , and therefore , as has been demonstrated , A : C :: B : D , and
inversely ( A. 5. ) C : A :: D : B. Therefore , & c . Q. E. D. PROP . C. THEOR . If the
first ...
Σελίδα 116
A + B has to C a greater ratio than A has to C ; and C has a greater ratio to A than
it has to A + B . Let m be such a number that mA and inB are each of them greater
than C ; and let nC be the least multiple of C that exceeds ma + mB ; then nC ...
A + B has to C a greater ratio than A has to C ; and C has a greater ratio to A than
it has to A + B . Let m be such a number that mA and inB are each of them greater
than C ; and let nC be the least multiple of C that exceeds ma + mB ; then nC ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common contained cosine cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular Euclid exterior extremity fall fore four fourth given given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism produced proportionals proposition proved Q. E. D. PROP radius ratio reason rectangle contained rectilineal figure right angles segment shewn sides similar sine solid square straight line taken tangent THEOR thing third touches triangle ABC wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 56 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Σελίδα 19 - 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 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.
Σελίδα 62 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Σελίδα 62 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
Σελίδα 130 - 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 76 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...
Σελίδα 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Σελίδα 18 - 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 55 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Πληροφορίες βιβλιογραφίας
| Τίτλος | Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added Elements of Plane and Spherical Trigonometry |
| Συγγραφέας | John Playfair |
| Επιμελητής | John Playfair |
| Μεταφράστηκε από | John Playfair |
| Έκδοση | 5 |
| Εκδότης | G. Long, 1819 |
| Πρωτότυπο από | το Πανεπιστήμιο του Μίτσιγκαν |
| Ψηφιοποιήθηκε στις | 11 Ιουν. 2007 |
| Μέγεθος | 333 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |