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 100.
Σελίδα 16
Wherefore from the given point A a straight line AL . has been drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . FROM the greater of two given straight lines to cut off a part equal to the less .
Wherefore from the given point A a straight line AL . has been drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . FROM the greater of two given straight lines to cut off a part equal to the less .
Σελίδα 17
Wherefore the whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the ...
Wherefore the whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the ...
Σελίδα 25
Wherefore , if at a point , & c . ... D and CEA , AED have been demonstrated to be equal to two right angles ; wherefore the angles CEA , AED are equal to the angles AED , DEB , Take away the common angle AED , and the remaining angle ...
Wherefore , if at a point , & c . ... D and CEA , AED have been demonstrated to be equal to two right angles ; wherefore the angles CEA , AED are equal to the angles AED , DEB , Take away the common angle AED , and the remaining angle ...
Σελίδα 33
1 . angle DEF , and the other angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle GCB is equal to the angle DFE ; but DFE is , by the hypothesis , equal to the angle BCA ; wherefore ...
1 . angle DEF , and the other angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle GCB is equal to the angle DFE ; but DFE is , by the hypothesis , equal to the angle BCA ; wherefore ...
Σελίδα 44
But the parallelogram ABCD is doubleb of the triangle ABC , because the diameter AC divides it into two equal parts ; wherefore ABCD is also double of the B с triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. OV PROP .
But the parallelogram ABCD is doubleb of the triangle ABC , because the diameter AC divides it into two equal parts ; wherefore ABCD is also double of the B с triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. OV PROP .
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Συχνά εμφανιζόμενοι όροι και φράσεις
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 |