Elements of geometry, based on Euclid, books i-iii1876 - 119 σελίδες |
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Σελίδα 55
... triangle and an angle , construct the triangle ... contained by the perpendicular distance between the parallel sides of the trapezium , and the sum of the parallel sides . 36. The area of any trapezium is half the rectangle EXERCISES . 55.
... triangle and an angle , construct the triangle ... contained by the perpendicular distance between the parallel sides of the trapezium , and the sum of the parallel sides . 36. The area of any trapezium is half the rectangle EXERCISES . 55.
Σελίδα 56
... triangle . 38. If the sides of a triangle be such that they are respectively the sum of two given lines , the difference of the same two lines , and twice the side of a square equal to the rectangle contained by these lines , the triangle ...
... triangle . 38. If the sides of a triangle be such that they are respectively the sum of two given lines , the difference of the same two lines , and twice the side of a square equal to the rectangle contained by these lines , the triangle ...
Σελίδα 58
... rectangle , or right - angled parallelogram , is said tɔ be contained by any two of the straight lines which contain one of the right angles . 2. In any parallelogram , the figure which is composed of either of the parallelograms about ...
... rectangle , or right - angled parallelogram , is said tɔ be contained by any two of the straight lines which contain one of the right angles . 2. In any parallelogram , the figure which is composed of either of the parallelograms about ...
Σελίδα 59
... contained by the two straight lines is equal to the rectangles contained by the un- divided line , and the several ... rectangle contained by the straight lines A and BC A · BC = shall be equal to the rectangle contained by A and BD , A ...
... contained by the two straight lines is equal to the rectangles contained by the un- divided line , and the several ... rectangle contained by the straight lines A and BC A · BC = shall be equal to the rectangle contained by A and BD , A ...
Σελίδα 60
... rectangle contained by AB and BC , together with the rectangle contained by AB and AC , shall be equal to the square on AB . CONSTRUCTION . - Upon AB describe the square ADEB ( I. 46 ) . Through , C draw CF parallel to AD or BE ( I. 31 ) ...
... rectangle contained by AB and BC , together with the rectangle contained by AB and AC , shall be equal to the square on AB . CONSTRUCTION . - Upon AB describe the square ADEB ( I. 46 ) . Through , C draw CF parallel to AD or BE ( I. 31 ) ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry, Based on Euclid, Βιβλία 1-3 Edward Atkins Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD angle ABC angle BAC angle BCD angle EDF angle equal base BC BC is equal bisect centre chord circle ABC circumference coincide common Const CONSTRUCTION describe diagonal diameter difference divided double draw drawn equal to CD exterior angle extremities fall figure four given point given rectilineal given straight line gnomon greater impossible join length less Let ABC Let the straight manner meet opposite angles parallel parallelogram pass perpendicular possible produced PROOF PROOF.-Because proved Q. E. D. Proposition rectangle contained right angles segment semicircle shown side BC sides square on AC Take taken third touches the circle triangle ABC twice the rectangle unequal
Δημοφιλή αποσπάσματα
Σελίδα 37 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are equal to two right angles.
Σελίδα 13 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC be produced to D and E.
Σελίδα 7 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 17 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 53 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Σελίδα 9 - 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 71 - 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 9 - Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another.
Σελίδα 34 - Wherefore, if a straight line, &c. QED PROPOSITION XXVIII. THEOREM. If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line ; or make the interior angles upon the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Σελίδα 69 - 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 half the line bisected, is equal to the square of the straight line, which is made up of the half and the part produced.