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 69.
Σελίδα 5
... proof is to be derived , is termed the hypothesis . A postulate is a problem so simple and easy in its nature , that it is unneces- sary to point out the method of performing it ; or in strictness , it is the demand of the author that ...
... proof is to be derived , is termed the hypothesis . A postulate is a problem so simple and easy in its nature , that it is unneces- sary to point out the method of performing it ; or in strictness , it is the demand of the author that ...
Σελίδα 11
... proof of this important proposition . When AB is applied to DE , it will coincide with it by the third definition . Also B will coincide with E , because AB is equal to DE . Were AB less than DE , B would fall between D and E ; but if ...
... proof of this important proposition . When AB is applied to DE , it will coincide with it by the third definition . Also B will coincide with E , because AB is equal to DE . Were AB less than DE , B would fall between D and E ; but if ...
Σελίδα 12
... given proceeds on the same general principle , but is shorter and easier . The proof would be equally easy were F and G taken in AB and AC . OTHERWISE Let the straight line AF divide the angle BAC 12 [ Book I. THE ELEMENTS.
... given proceeds on the same general principle , but is shorter and easier . The proof would be equally easy were F and G taken in AB and AC . OTHERWISE Let the straight line AF divide the angle BAC 12 [ Book I. THE ELEMENTS.
Σελίδα 13
... proof is perfectly satisfactory ; and on account of its ease and sim- plicity , it may perhaps be preferred by those who are reading the Elements for the first time . This proposition may also be proved by conceiving the triangle BAC to ...
... proof is perfectly satisfactory ; and on account of its ease and sim- plicity , it may perhaps be preferred by those who are reading the Elements for the first time . This proposition may also be proved by conceiving the triangle BAC to ...
Σελίδα 14
... proof by supposing AC , greater than AB . It would perhaps remove in some degree the difficulty which beginners often feel in respect to negative demonstrations , were they expressed hypothetically . Thus , in the present instance , we ...
... proof by supposing AC , greater than AB . It would perhaps remove in some degree the difficulty which beginners often feel in respect to negative demonstrations , were they expressed hypothetically . Thus , in the present instance , we ...
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...