The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Αποτελέσματα 1 - 5 από τα 34.
Σελίδα 2
... angle which is contained by the straight lines ab , cb , is named the angle abc , or cba ; that which is contained by ab , db , is named the angle abd , or dba ; and that which is con- tained by db , cb , is called the angle d bc , or ...
... angle which is contained by the straight lines ab , cb , is named the angle abc , or cba ; that which is contained by ab , db , is named the angle abd , or dba ; and that which is con- tained by db , cb , is called the angle d bc , or ...
Σελίδα 5
... cb , are each of them equal to ab ; but things which are equal to the same are equal to one another ( 1 ax . ) ; therefore ca is equal to cb ; wherefore ca , ab , bc are equal to one another ; and the tri- angle abc is therefore ...
... cb , are each of them equal to ab ; but things which are equal to the same are equal to one another ( 1 ax . ) ; therefore ca is equal to cb ; wherefore ca , ab , bc are equal to one another ; and the tri- angle abc is therefore ...
Σελίδα 6
... angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle a bc to the angle def , and the angle a cb to dfe . Therefore , if two triangles have two sides of the one equal to two ...
... angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle a bc to the angle def , and the angle a cb to dfe . Therefore , if two triangles have two sides of the one equal to two ...
Σελίδα 7
... cb , each to each ; and the angle dbc is equal to the angle acb ; therefore the base dc is equal to the base ab , and the triangle db c is equal to the triangle ( i . 4 ) a cb , the less to the greater ; which is absurd . Therefore ab ...
... cb , each to each ; and the angle dbc is equal to the angle acb ; therefore the base dc is equal to the base ab , and the triangle db c is equal to the triangle ( i . 4 ) a cb , the less to the greater ; which is absurd . Therefore ab ...
Σελίδα 8
... angle bcd ; therefore the angle adc is greater also than bcd ; much greater then is the angle bd c than the angle bcd . Again , because cb is equal to db , the angle bdc is equal ( i . 5 ) to the angle bcd ; but it has been demonstrated ...
... angle bcd ; therefore the angle adc is greater also than bcd ; much greater then is the angle bd c than the angle bcd . Again , because cb is equal to db , the angle bdc is equal ( i . 5 ) to the angle bcd ; but it has been demonstrated ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc describe diameter double draw equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment semicircle shewn square of a c straight line a b straight line ab straight line bc straight line drawn tiple touches the circle triangle abc triangle def twice the rectangle
Δημοφιλή αποσπάσματα
Σελίδα 2 - 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 42 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Σελίδα 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 21 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Σελίδα 29 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 38 - 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, together with the square of...
Σελίδα 15 - If, from the ends of the 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. Let...
Σελίδα 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 4 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 126 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.