The elements of plane geometry; or, The first six books of Euclid, ed. by W. Davis |
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Αποτελέσματα 1 - 5 από τα 21.
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 . XVI .
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 . XVI .
Σελίδα 37
Produce D E to meet the circumference in H. The square described upon EH is equal to the given rectilineal figure A. Join GH . Because the straight line BF is divided into two equal parts at G , and into two unequal parts at E ...
Produce D E to meet the circumference in H. The square described upon EH is equal to the given rectilineal figure A. Join GH . Because the straight line BF is divided into two equal parts at G , and into two unequal parts at E ...
Σελίδα 38
Circles are said to touch one another when their circumferences meet in any point , but do not cut one another . IV . ... The angle of a segment is that which is contained by the straight line and the circumference . VIII .
Circles are said to touch one another when their circumferences meet in any point , but do not cut one another . IV . ... The angle of a segment is that which is contained by the straight line and the circumference . VIII .
Σελίδα 39
X. A sector of a circle is the figure contained by two ( radii , or ) straight lines drawn from the centre , and the arc , or part of the circumference between them . XI . Similar segments of circles are those in which the angles are ...
X. A sector of a circle is the figure contained by two ( radii , or ) straight lines drawn from the centre , and the arc , or part of the circumference between them . XI . Similar segments of circles are those in which the angles are ...
Σελίδα 41
Join FC , and draw any straight line FEB , cutting their circumferences at E and B. Because F is the centre of the ... be drawn to the circumference , the greatest is that ( FA ) which passes through the centre ; the remainder of that ...
Join FC , and draw any straight line FEB , cutting their circumferences at E and B. Because F is the centre of the ... be drawn to the circumference , the greatest is that ( FA ) which passes through the centre ; the remainder of that ...
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Άλλες εκδόσεις - Προβολή όλων
The Elements of Plane Geometry; Or, the First Six Books of Euclid. From the ... Πλήρης προβολή - 1863 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD alternate angle ABC angle BAC angle BCD base base BC bisected centre circle ABC circumference common described divided double draw drawn equal angles equal Ax equal Const equiangular equimultiples exterior angle extremities fore fourth given given straight line greater greater ratio half impossible inscribed interior join less magnitudes manner meet multiple opposite angle parallel parallelogram pass perpendicular PROBLEM.)-To produced proportionals proved Q. E. D. PROP reason rectangle rectangle contained rectilineal figure remaining angle right angles segment shown side BC sides similar square square of AC straight line AC Take taken THEOREM.)-If third touches the circle triangle ABC unequal Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 3 - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. VIII. A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.
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 : XVI.
Σελίδα 67 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Σελίδα 12 - 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 93 - From this it is manifest, that the perpendicular drawn from the right angle of a right-angled triangle to the base, is a mean proportional between the segments of the base; and also that each of the sides is a mean proportional between the base, and...
Σελίδα 68 - This 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 ; or that the first is to the third as the second to the fourth : as is shown in Prop.
Σελίδα 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 88 - From this it is plain, that triangles and parallelograms that have equal altitudes, are to one another as their bases. Let the figures be placed so as to have their bases in the same straight line; and having drawn perpendiculars from the vertices of the triangles to the bases, the straight line which joins the vertices is parallel to that in which their bases are, (I.
Σελίδα 69 - This term is used when the first magnitude is to the second of the first rank, as the last but one is to the last of the second rank; and as the second is to the third of the first rank, so is the last but two to the last but one of the second rank; and as the third is to the fourth of the first rank, so is the third from the last to the last but two of the second rank; and so on in a cross order: and the inference is as in the 18th definition.
Σελίδα 21 - ... figure, together with four right angles, are equal to twice as many right angles as the figure has be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Πληροφορίες βιβλιογραφίας
| Τίτλος | The elements of plane geometry; or, The first six books of Euclid, ed. by W. Davis |
| Συγγραφέας | Euclides |
| Επιμελητής | William Davis (B.A.) |
| Εκδόθηκε | 1863 |
| Πρωτότυπο από | Πανεπιστήμιο Οξφόρδης |
| Ψηφιοποιήθηκε στις | 21 Νοεμ. 2006 |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |