Elements of Geometry...: Translated from the French for the Use of the Students of the University at Cambridge, New EnglandHilliard and Metcalf, 1825 - 224 σελίδες |
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Σελίδα v
... suppose that there can be only one between the same points . It is upon this principle , considered at the same time as a definition and an axiom , that I have endeavoured to established the entire edifice of the elements . It is ...
... suppose that there can be only one between the same points . It is upon this principle , considered at the same time as a definition and an axiom , that I have endeavoured to established the entire edifice of the elements . It is ...
Σελίδα xiv
... suppose one of these lines , or a fifth , if we please , to answer as a common measure to the whole , and to be taken for unity ; then A , B , C , D , will each represent a certain number of units , entire or frac- tional ...
... suppose one of these lines , or a fifth , if we please , to answer as a common measure to the whole , and to be taken for unity ; then A , B , C , D , will each represent a certain number of units , entire or frac- tional ...
Σελίδα 4
... suppose , if it be pos- sible , that it falls upon a line CK , different from CD ; since , by hypothesis ( 10 ) , the angle EGH = HGF , it follows that Fig . 17 . But and besides , by hypothesis , hence ACK KCB . ACK ACD , KCB BCD ; ACD ...
... suppose , if it be pos- sible , that it falls upon a line CK , different from CD ; since , by hypothesis ( 10 ) , the angle EGH = HGF , it follows that Fig . 17 . But and besides , by hypothesis , hence ACK KCB . ACK ACD , KCB BCD ; ACD ...
Σελίδα 5
... suppose , if it be possible , that the lines , when produced , separate from each other at a point C , the one becoming CD , and the other CE . At the point C , let CF be drawn , so as to make the angle ACF , a right angle ; then , ACD ...
... suppose , if it be possible , that the lines , when produced , separate from each other at a point C , the one becoming CD , and the other CE . At the point C , let CF be drawn , so as to make the angle ACF , a right angle ; then , ACD ...
Σελίδα 26
... suppose that they are parallel ; the line AB perpendicular to DE will be perpendicular to FG ( 65 ) , and the angle K will be a right angle ; but BK , which is BD pro- duced , is different from BF , since the three points A , B , C ...
... suppose that they are parallel ; the line AB perpendicular to DE will be perpendicular to FG ( 65 ) , and the angle K will be a right angle ; but BK , which is BD pro- duced , is different from BF , since the three points A , B , C ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry...: Translated from the French for the Use of the ... Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2020 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circle circular sector circumference circumscribed common cone consequently construction convex surface Corollary cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent figure formed four right angles frustum Geom given point gles greater hence homologous sides hypothenuse hypothesis inclination inscribed isosceles join less let fall line AC measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN point F polyedron prism proposition quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium sector segment semicircumference side AC sides AB similar solid angle sphere spherical polygons spherical triangle straight line tangent THEOREM third side triangle ABC triangles are equal triangular prism triangular pyramids vertex vertices whence
Δημοφιλή αποσπάσματα
Σελίδα 43 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Σελίδα 3 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Σελίδα 4 - Hence a straight line drawn from the vertex of an isosceles triangle, to the middle of the base, is perpendicular to that base, and divides the vertical angle into two equal parts.
Σελίδα 16 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Σελίδα 58 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Σελίδα 158 - CD, &c., taken together, make up the perimeter of the prism's base : hence the sum of these rectangles, or the convex surface of the prism, is equal to the perimeter of its base multiplied by its altitude.
Σελίδα 32 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Σελίδα 142 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Σελίδα 136 - The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle; produce the sides AB, AU, till they meet again in D.
Σελίδα 154 - ABCDE, and equal in altitude to the cylinder, is said to be inscribed in the cylinder, or the cylinder to be circumscribed about the prism.