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 27.
Σελίδα 43
... a square upon AB . D - - A From the point A draw ( I . 11 . ) AC at right angles to
AB , and make ( I . 3 . ) AD equal to AB , and through the point D draw DE parallel
( I . 31 . ) to AB , and through B draw BE parallel to AD ; therefore ( I . 34 . Def . ) ...
... a square upon AB . D - - A From the point A draw ( I . 11 . ) AC at right angles to
AB , and make ( I . 3 . ) AD equal to AB , and through the point D draw DE parallel
( I . 31 . ) to AB , and through B draw BE parallel to AD ; therefore ( I . 34 . Def . ) ...
Σελίδα 44
... which contain the right angle . Let ABC be a right - angled triangle having the
right angle BAC ; the square described upon the side BC ' is equal to the squares
described upon BA , AC . I . B L On BC describe ( I . 46 . ) the square BDEC , and
...
... which contain the right angle . Let ABC be a right - angled triangle having the
right angle BAC ; the square described upon the side BC ' is equal to the squares
described upon BA , AC . I . B L On BC describe ( I . 46 . ) the square BDEC , and
...
Σελίδα 45
The square upon the side BC is equal to the squares upon the sides BĂ , AC .
Therefore , in any right - angled triangle , & c . Q . E . D . PROP . XLVIII . —
THEOREM . If the square described upon one of the sides of a triangle , be equal
to the ...
The square upon the side BC is equal to the squares upon the sides BĂ , AC .
Therefore , in any right - angled triangle , & c . Q . E . D . PROP . XLVIII . —
THEOREM . If the square described upon one of the sides of a triangle , be equal
to the ...
Σελίδα 46
To each of these add the square of AC ; therefore 2 . The squares of DA , AC , are
equal to the squares of BA , AC . But ( I . 47 . ) 3 . The square of DC is equal to the
squares of DA , AC , because DAC is a right angle ; and the square of BC , by ...
To each of these add the square of AC ; therefore 2 . The squares of DA , AC , are
equal to the squares of BA , AC . But ( I . 47 . ) 3 . The square of DC is equal to the
squares of DA , AC , because DAC is a right angle ; and the square of BC , by ...
Σελίδα 48
Let the straight line AB be divided into any two parts in the point C ; the rectangle
contained by AB , BC , together with the rectangle * AB , AC , shall be equal to the
square of AB . CI TE Upon AB describe ( I . 46 . ) the square ADEB , and ...
Let the straight line AB be divided into any two parts in the point C ; the rectangle
contained by AB , BC , together with the rectangle * AB , AC , shall be equal to the
square of AB . CI TE Upon AB describe ( I . 46 . ) the square ADEB , and ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal angle ABC angle ACB angle BAC angle BCD angle equal base 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 Let the straight likewise manner meet opposite angles parallel parallelogram pass pentagon perpendicular point F PROBLEM produced Q.E.D. PROP reason rectangle contained rectilineal figure remaining angle required to describe right angles segment semicircle shown 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 |