The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illus., and an Appendix in Five Books |
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Σελίδα 1
A point is that which has position , but not magnitude . + 2. A line is length without breadth . Corollary . The extremities of a line are points ; and an intersection of one line with another is also a point . I 3.
A point is that which has position , but not magnitude . + 2. A line is length without breadth . Corollary . The extremities of a line are points ; and an intersection of one line with another is also a point . I 3.
Σελίδα 4
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.t F D E A B H a 31.
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.t F D E A B H a 31.
Σελίδα 5
Let it be granted , that a straight line may be drawn from any one point , to any other point : t ou it . writers rather improperly use arch ) and chord receive their names from the bow ( in Latin arcus ) , and its cord or string .
Let it be granted , that a straight line may be drawn from any one point , to any other point : t ou it . writers rather improperly use arch ) and chord receive their names from the bow ( in Latin arcus ) , and its cord or string .
Σελίδα 8
the circle ACE ; and from the point c , in which the circles cut one another , draw ( 1 . post . 1. ) the straight lines CA , CB to the points A ... Because the point A is the centre of the circle BCD , AC is equal ( I. definition 30. ) ...
the circle ACE ; and from the point c , in which the circles cut one another , draw ( 1 . post . 1. ) the straight lines CA , CB to the points A ... Because the point A is the centre of the circle BCD , AC is equal ( I. definition 30. ) ...
Σελίδα 9
Wherefore from the given point A a straight line AF has been drawn equal to the given straight line BC : which was to be done . PROP . III . PROB . D A E B From the greater of two given straight lines to cut off a part equal to the ...
Wherefore from the given point A a straight line AF has been drawn equal to the given straight line BC : which was to be done . PROP . III . PROB . D A E B From the greater of two given straight lines to cut off a part equal to the ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude base bisected called centre chord circle circumference coincide common cone consequently const construction contained continual cylinder demonstrated describe diagonal diameter difference divided double draw equal equal angles extremities figure fore four fourth given given circle given point given straight line greater half Hence inscribed join less magnitudes manner means meet method multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced proof PROP proportional proposition proved pyramid radius ratio reason rectangle remaining respectively right angles Schol segments semicircle shown sides similar square straight line taken THEOR third touching triangle triangle ABC twice vertical wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 94 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 53 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 143 - 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 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Σελίδα 57 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
Σελίδα 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Σελίδα 43 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Σελίδα 32 - 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 40 - 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 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Πληροφορίες βιβλιογραφίας
| Τίτλος | The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illus., and an Appendix in Five Books |
| Συγγραφέας | Euclid |
| Επιμελητής | James Thomson |
| Έκδοση | 2 |
| Εκδότης | Adam and Charles Black, 1837 |
| Πρωτότυπο από | το Πανεπιστήμιο του Μίτσιγκαν |
| Ψηφιοποιήθηκε στις | 15 Μάιος 2008 |
| Μέγεθος | 390 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |