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 8
... BC is equal ( I. def . 30. ) to BA . But it has been proved that CA is equal to AB ; therefore CА , СВ are each of them equal to AB : but things which are equal to the same are equal ( I. axiom 1. ) to one another ; therefore CA is ...
... BC is equal ( I. def . 30. ) to BA . But it has been proved that CA is equal to AB ; therefore CА , СВ are each of them equal to AB : but things which are equal to the same are equal ( I. axiom 1. ) to one another ; therefore CA is ...
Σελίδα 9
... equal ( I. ax . 3. ) to the remainder BE . But it has been shown , that BC is equal to BE ; wherefore AF and BC are each of them equal to BE ; and things that are equal to the same are equal ( I. ax . 1. ) to one another ; therefore the ...
... equal ( I. ax . 3. ) to the remainder BE . But it has been shown , that BC is equal to BE ; wherefore AF and BC are each of them equal to BE ; and things that are equal to the same are equal ( I. ax . 1. ) to one another ; therefore the ...
Σελίδα 11
... equal to the angle EDF ; where- fore also the point C shall coincide with the point F , because ( hyp . ) AC is equal to DF . But the point B coincides with E ; wherefore the base BC ... BC did not coincide with EF , two straight lines ...
... equal to the angle EDF ; where- fore also the point C shall coincide with the point F , because ( hyp . ) AC is equal to DF . But the point B coincides with E ; wherefore the base BC ... BC did not coincide with EF , two straight lines ...
Σελίδα 15
... equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal ( I. 5. ) to one ... BC equal to the base EF ; the angle BAC is equal to the angle EDF , B and the two triangles are equal in area ...
... equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal ( I. 5. ) to one ... BC equal to the base EF ; the angle BAC is equal to the angle EDF , B and the two triangles are equal in area ...
Σελίδα 16
... equal to it . Therefore , if two triangles , & c . OTHERWISE . A D E F C G 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 it . Therefore , if two triangles , & c . OTHERWISE . A D E F C G 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 ...
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 scholium 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...