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 1 - 5 από τα 100.
Σελίδα 10
... Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides , DE , DF , each to each , viz . , AB to DE , and AC to DF ; and the angle BAC equal to the angle EDF : then ( 1. ) the base BC is equal to the base ...
... Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides , DE , DF , each to each , viz . , AB to DE , and AC to DF ; and the angle BAC equal to the angle EDF : then ( 1. ) the base BC is equal to the base ...
Σελίδα 12
... Let ABC be an isosceles triangle , of which the side AB is equal to AC , and let the sides AB , AC be produced to D and E ; the angle ABC is equal to the angle ACB , and the angle CBD to the angle BCE . D F B C R In BD + take any point ...
... Let ABC be an isosceles triangle , of which the side AB is equal to AC , and let the sides AB , AC be produced to D and E ; the angle ABC is equal to the angle ACB , and the angle CBD to the angle BCE . D F B C R In BD + take any point ...
Σελίδα 13
... ABC be a triangle having the angle ABC equal to the angle ACB ; the side AB is also equal to the side AC . For , if AB be not equal to AC , ‡ one of them is greater than * Through the point ... let AB be the greater Book I. ] 13 OF EUCLID .
... ABC be a triangle having the angle ABC equal to the angle ACB ; the side AB is also equal to the side AC . For , if AB be not equal to AC , ‡ one of them is greater than * Through the point ... let AB be the greater Book I. ] 13 OF EUCLID .
Σελίδα 15
... Let ABC , DEF be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . , AB to DE , and AC to DF ; and also the base BC equal to the base EF ; the angle BAC is equal to the angle EDF , B and ...
... Let ABC , DEF be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . , AB to DE , and AC to DF ; and also the base BC equal to the base EF ; the angle BAC is equal to the angle EDF , B and ...
Σελίδα 16
... Let the triangle ABC be inverted with respect to the base BC , and let BC be applied to EF , so that B may fall on E ; then will C coincide with F , because BC is equal to EF ; and the tri- angle ABC will take the position GEF , EG ...
... Let the triangle ABC be inverted with respect to the base BC , and let BC be applied to EF , so that B may fall on E ; then will C coincide with F , because BC is equal to EF ; and the tri- angle ABC will take the position GEF , EG ...
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...