The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good1853 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 6 - 10 από τα 32.
Σελίδα 31
... shown to be equal to the angle BAC ; therefore ( Ax . 2. ) 3. The whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to each of these equals add the angle ACB ; BOOK I. - PROP . XXXI . XXXII . 31.
... shown to be equal to the angle BAC ; therefore ( Ax . 2. ) 3. The whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to each of these equals add the angle ACB ; BOOK I. - PROP . XXXI . XXXII . 31.
Σελίδα 33
... shown to be equal to it . Therefore , straight lines , & c . Q.E.D. PROP . XXXIV . - THEOREM . The opposite sides and angles of parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two ...
... shown to be equal to it . Therefore , straight lines , & c . Q.E.D. PROP . XXXIV . - THEOREM . The opposite sides and angles of parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two ...
Σελίδα 34
... shown to be equal to the angle BDC ; therefore the opposite sides and angles of parallelograms are equal to one another . Also , their diameter bisects them ; for AB being equal to CD , and BC common , the two AB , BC , are equal to the ...
... shown to be equal to the angle BDC ; therefore the opposite sides and angles of parallelograms are equal to one another . Also , their diameter bisects them ; for AB being equal to CD , and BC common , the two AB , BC , are equal to the ...
Σελίδα 66
... shown , that no other point but F is the centre ; that is 5. F is the centre of the circle ABC . Which was to be found . COR . From this it is manifest , that if in a circle a straight line bisect another at right angles , the centre of ...
... shown , that no other point but F is the centre ; that is 5. F is the centre of the circle ABC . Which was to be found . COR . From this it is manifest , that if in a circle a straight line bisect another at right angles , the centre of ...
Σελίδα 69
... shown to be a right angle ; therefore 3. FEA is equal to the angle FEB , the less to the greater , which is impossible : therefore 4. AC , BD , do not bisect one another . Wherefore , if in a circle , & c . Q.E.D. PROP . V. - THEOREM ...
... shown to be a right angle ; therefore 3. FEA is equal to the angle FEB , the less to the greater , which is impossible : therefore 4. AC , BD , do not bisect one another . Wherefore , if in a circle , & c . Q.E.D. PROP . V. - THEOREM ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal adjacent angles AF is equal angle ABC angle ACB angle AGH angle BAC angle BCD angle DEF angle EAB angle EDF angle equal base BC bisected circle ABC cuts the circle describe a circle diameter double equal angles equal Constr equal Hyp equal straight lines equal to BC equiangular equilateral and equiangular EUCLID'S ELEMENTS exterior angle given circle given rectilineal angle given straight line given triangle gnomon greater inscribed join Let ABC Let the straight likewise opposite angles parallel to CD parallelogram pentagon perpendicular point F Q.E.D. PROP rectangle AD rectangle AE rectangle contained rectilineal figure remaining angle required to describe right angles semicircle side BC square of AC straight line AB straight line AC touches the circle triangle ABC triangle DEF twice the rectangle
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...