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 39.
Σελίδα 2
... solid , is that which has length , breadth , and thickness . Cor . The extremities of a body are surfaces . 7. A ... angles equal to one another , each of the angles is called a right angle ; and the straight line which stands on ...
... solid , is that which has length , breadth , and thickness . Cor . The extremities of a body are surfaces . 7. A ... angles equal to one another , each of the angles is called a right angle ; and the straight line which stands on ...
Σελίδα 100
... solids , and angles form three other classes of homogeneous magnitudes . On the contrary , lines and surfaces , lines and angles , surfaces and solids , & c . , are heterogeneous . Thus , it is obviously improper to say , that the side ...
... solids , and angles form three other classes of homogeneous magnitudes . On the contrary , lines and surfaces , lines and angles , surfaces and solids , & c . , are heterogeneous . Thus , it is obviously improper to say , that the side ...
Σελίδα 174
... angles with all straight lines meeting it in that plane . 2. The inclination of two planes which meet one another ... solid angle is that which is made by more than two plane angles meeting in one point , and not lying in the same ...
... angles with all straight lines meeting it in that plane . 2. The inclination of two planes which meet one another ... solid angle is that which is made by more than two plane angles meeting in one point , and not lying in the same ...
Σελίδα 184
... angles to the plane CK ; therefore ( XI . 8. ) FG is also at right angles to the same plane . plane is at right ... solid angle be contained by three plane angles , any two of them are greater than the third . D Let the solid angle ...
... angles to the plane CK ; therefore ( XI . 8. ) FG is also at right angles to the same plane . plane is at right ... solid angle be contained by three plane angles , any two of them are greater than the third . D Let the solid angle ...
Σελίδα 185
... solid angle , & c . PROP . XXI . THEOR . " EVERY solid angle is contained by plane angles , which together are less than four right angles . Let the solid angle at A be contained by any number of plane angles BAC , CAD , DAE , EAF , FAB ...
... solid angle , & c . PROP . XXI . THEOR . " EVERY solid angle is contained by plane angles , which together are less than four right angles . Let the solid angle at A be contained by any number of plane angles BAC , CAD , DAE , EAF , FAB ...
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...