The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illustrations, and an Appendix in Five BooksA. & C. Black, 1837 - 390 σελίδες |
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Αποτελέσματα 6 - 10 από τα 100.
Σελίδα 14
... greater , and from it cut off DB equal to AC , the less , and join DC . Then because in the tri- angles DBC , ACB , DB is equal to AC , and BC com- mon to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and ...
... greater , and from it cut off DB equal to AC , the less , and join DC . Then because in the tri- angles DBC , ACB , DB is equal to AC , and BC com- mon to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and ...
Σελίδα 15
... greater is impossible . than it ; which A D E P B But if one of the vertices , as D , be within the other triangle ... greater ( I. ax . 9. ) than BCD ; wherefore the angle FDC is likewise greater than BCD : much more then is BDC greater ...
... greater is impossible . than it ; which A D E P B But if one of the vertices , as D , be within the other triangle ... greater ( I. ax . 9. ) than BCD ; wherefore the angle FDC is likewise greater than BCD : much more then is BDC greater ...
Σελίδα 18
... greater than DC , and to join their point of intersection with C. The proof follows from the construction and the eighth proposition . It will be a check on the manual operation , if intersections be made on both sides of AB , as these ...
... greater than DC , and to join their point of intersection with C. The proof follows from the construction and the eighth proposition . It will be a check on the manual operation , if intersections be made on both sides of AB , as these ...
Σελίδα 21
... greater ( I. ax . 9. ) than ECF ; therefore the angle ACD is greater than BAE . In the same manner , if the side AC be produced ( I. post . 2. ) to G , and BC be bisected in H , and if a straight line be drawn from A to H and produced ...
... greater ( I. ax . 9. ) than ECF ; therefore the angle ACD is greater than BAE . In the same manner , if the side AC be produced ( I. post . 2. ) to G , and BC be bisected in H , and if a straight line be drawn from A to H and produced ...
Σελίδα 22
... greater ( I. ax . 4. ) than ABC , ACB ; but ACD , ACB are together equal ( I. 13. ) to two right angles ; therefore ... greater side has the greater angle opposite to it . Let ABC be a triangle , of which the side AC is greater than the ...
... greater ( I. ax . 4. ) than ABC , ACB ; but ACD , ACB are together equal ( I. 13. ) to two right angles ; therefore ... greater side has the greater angle opposite to it . Let ABC be a triangle , of which the side AC is greater than the ...
Άλλες εκδόσεις - Προβολή όλων
The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol segments semicircle sides similar similar triangles solid angles square of AC straight lines drawn tangent THEOR third triangle ABC triplicate ratio vertex vertical angle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 94 - 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.
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. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 143 - 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.
Σελίδα 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Σελίδα 57 - 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 on the other part.
Σελίδα 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Σελίδα 43 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right 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 40 - 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 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...