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 21.
Σελίδα 44
The figure ADEB is rectangular , and it has been demonstrated that it is equilateral ; therefore ( Def . 30. ) ... upon the side subtending the right angle , is equal to the squares described upon the sides which contain the right angle .
The figure ADEB is rectangular , and it has been demonstrated that it is equilateral ; therefore ( Def . 30. ) ... upon the side subtending the right angle , is equal to the squares described upon the sides which contain the right angle .
Σελίδα 47
I. Every right - angled parallelogram , or rectangle , is said to be contained by any two of the straight lines which contain one of the right angles . II . In every parallelogram , any of the parallelograms about a diameter , together ...
I. Every right - angled parallelogram , or rectangle , is said to be contained by any two of the straight lines which contain one of the right angles . II . In every parallelogram , any of the parallelograms about a diameter , together ...
Σελίδα 48
A , BC , is equal to the rectangle contained by A , BD , together with that contained by A , DE , and that contained by A , EC . B D E C G K L H F A From the point B draw ( I. 11. ) BF at right angles to BC , and make BG equal ( 1.3 . ) ...
A , BC , is equal to the rectangle contained by A , BD , together with that contained by A , DE , and that contained by A , EC . B D E C G K L H F A From the point B draw ( I. 11. ) BF at right angles to BC , and make BG equal ( 1.3 . ) ...
Σελίδα 49
CF parallel to AD or BE ; then AE is equal to the rectangles AF , CE ; and AE is the square of AB ; and 1. AF is the rectangle contained by BA , AC , for it is contained by DA , AC , of which AD is equal ( Def . 30. ) to AB ; and 2.
CF parallel to AD or BE ; then AE is equal to the rectangles AF , CE ; and AE is the square of AB ; and 1. AF is the rectangle contained by BA , AC , for it is contained by DA , AC , of which AD is equal ( Def . 30. ) to AB ; and 2.
Σελίδα 50
Let the straight line AB be divided into any two parts in C ; the square of AB is equal to the squares of AC , CB , together with twice the rectangle contained by AC , CB . H G K D F E Upon AB describe ( I. 46. ) ...
Let the straight line AB be divided into any two parts in C ; the square of AB is equal to the squares of AC , CB , together with twice the rectangle contained by AC , CB . H G K D F E Upon AB describe ( I. 46. ) ...
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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 |