The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. 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 |
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Αποτελέσματα 1 - 5 από τα 54.
Σελίδα 119
Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . V. The first of four magnitudes is said to have the same ratio to the second , which the third has to the fourth , when any ...
Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . V. The first of four magnitudes is said to have the same ratio to the second , which the third has to the fourth , when any ...
Σελίδα 120
Book V. or , if the multiple of the first be greater than that of the second , the multiple of the third is also greater than that of the fourth . VI . Magnitudes which have the same ratio are called proportionals .
Book V. or , if the multiple of the first be greater than that of the second , the multiple of the third is also greater than that of the fourth . VI . Magnitudes which have the same ratio are called proportionals .
Σελίδα 121
Permutando , or alternando , by premutation , or alternately ; this See Note . word is used when there are four proportionals , and it is inferred , that the first has the same ratio to the third , which the second has to the fourth ...
Permutando , or alternando , by premutation , or alternately ; this See Note . word is used when there are four proportionals , and it is inferred , that the first has the same ratio to the third , which the second has to the fourth ...
Σελίδα 122
Book V. second , as the third to its excess above the fourth . Prop . L , book 5 . XVIII . Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance ; when there is any number of magnitudes more than two , and as many others ...
Book V. second , as the third to its excess above the fourth . Prop . L , book 5 . XVIII . Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance ; when there is any number of magnitudes more than two , and as many others ...
Σελίδα 124
If the first magnitude be the same multiple of the second that the third is of the fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same ...
If the first magnitude be the same multiple of the second that the third is of the fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same ...
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ABCD added altitude angle ABC angle BAC arch base Book centre circle circle ABC circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 17 - FG; then, upon the same base EF, and upon the same side of it, there can be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise their sides terminated in the other extremity: But this is impossible (i.
Σελίδα 35 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 67 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.
Σελίδα 92 - IF a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Σελίδα 26 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.
Σελίδα 55 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line, which is made of the whole and that part.
Σελίδα 318 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Σελίδα 22 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Σελίδα 161 - If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.
Σελίδα 21 - 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.
Πληροφορίες βιβλιογραφίας
| Τίτλος | The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. 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 |
| Συγγραφέας | Euclid |
| Εκδότης | Conrad and Company, 1810 |
| Πρωτότυπο από | η Δημόσια Βιβλιοθήκη της Νέας Υόρκης |
| Ψηφιοποιήθηκε στις | 21 Ιουν. 2006 |
| Μέγεθος | 518 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |