The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good |
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Αποτελέσματα 1 - 5 από τα 17.
Σελίδα 2
... 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 . XI . An obtuse angle is that which is greater than a right angle .
... 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 . XI . An obtuse angle is that which is greater than a right angle .
Σελίδα 16
To draw a straight line perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight line , which may be produced to any length both ways , and let C be a point without it ...
To draw a straight line perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight line , which may be produced to any length both ways , and let C be a point without it ...
Σελίδα 60
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 ...
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 ...
Σελίδα 61
the perpendicular AD from the opposite angle : the square of AC opposite to the angle B , is less than the squares of CB , BA , by twice the rectangle CB , BD . B D C First , let AD fall within the triangle ABC ; and because the ...
the perpendicular AD from the opposite angle : the square of AC opposite to the angle B , is less than the squares of CB , BA , by twice the rectangle CB , BD . B D C First , let AD fall within the triangle ABC ; and because the ...
Σελίδα 62
Lastly , let the side AC be perpendicular to BC . B C Then BC is the straight line between the perpendicular and the acute angle at B ; and it is manifest that ( I. 47. ) A The squares of AB , BC , are equal to the square of AC ...
Lastly , let the side AC be perpendicular to BC . B C Then BC is the straight line between the perpendicular and the acute angle at B ; and it is manifest that ( I. 47. ) A The squares of AB , BC , are equal to the square of AC ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal AF is equal angle ABC angle ACB angle BAC angle BCD angle equal base BC bisected centre circle ABC circumference coincide common demonstrated describe diameter distance divided double draw equal angles equal Constr exterior angle extremity fall figure four given circle given point given straight line given triangle greater impossible inscribed join less Let ABC likewise manner meet opposite angles parallel parallelogram pass pentagon perpendicular point F produced Q.E.D. PROP reason rectangle contained rectilineal figure remaining angle required to describe right angles segment semicircle shown side BC sides square of AC straight line AC touches the circle triangle ABC twice the rectangle wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 26 - 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. either the sides adjacent to the equal...
Σελίδα 22 - 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 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 1 - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. vm. "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 97 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 7 - AB; but things which are equal to the same are equal to one another...
Σελίδα 14 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.
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.
Σελίδα 41 - 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 52 - If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced...
Πληροφορίες βιβλιογραφίας
| Τίτλος | The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good |
| Συγγραφέας | Euclides |
| Επιμελητής | Samuel A Good |
| Εκδόθηκε | 1853 |
| Πρωτότυπο από | Πανεπιστήμιο Οξφόρδης |
| Ψηφιοποιήθηκε στις | 7 Σεπτ. 2006 |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |