Elements of GeometryHilliard and Metcalf, at the University Press, 1819 - 208 σελίδες |
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Αποτελέσματα 1 - 5 από τα 91.
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 establish 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 establish 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 fractional , commen ...
... 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 fractional , commen ...
Σελίδα 4
... suppose , if it be possible , that it falls upon a line CK , different from CD ; since , by hypo- EGH = HGF , thesis ( 10 ) , the angle it follows that ACK = KCB . Fig . 17 . But and besides , by hypothesis , hence ACK > ACD , KCB BCD ...
... suppose , if it be possible , that it falls upon a line CK , different from CD ; since , by hypo- EGH = HGF , thesis ( 10 ) , the angle it follows that ACK = KCB . Fig . 17 . But and besides , by hypothesis , hence ACK > ACD , KCB BCD ...
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 Kwill be a right angle ; but BK , which is BD pro- duced , is different from BF , since the three points A , B , C , are ...
... suppose that they are parallel ; the line AB perpendicular to DE will be perpendicular to FG ( 65 ) , and the angle Kwill be a right angle ; but BK , which is BD pro- duced , is different from BF , since the three points A , B , C , are ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles algebraic algebraic quantities altitude angle ACB base centre chord circ circle circular sector circumference coefficient common divisor cone consequently contains Corollary cube cylinder Demonstration denominator denoted diameter divided dividend division equal equivalent evident example exponent expression factors figure fraction frustum given gives greater greatest common divisor homologous sides inscribed less letters logarithm manner measure multiplied obtain parallel parallelogram parallelopiped perpendicular plane MN polyedron preceding prism proportion proposed equation proposition quotient radical sign radii radius ratio rectangle reduced regular polygon remainder result right angles Scholium side BC similar solid angle sphere spherical square root straight line substitute subtract suppose term THEOREM third tion triangle ABC triangular pyramids unity unknown quantity vertex whence
Δημοφιλή αποσπάσματα
Σελίδα 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Σελίδα 7 - 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 151 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Σελίδα 76 - 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 25 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Σελίδα 52 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Σελίδα 160 - 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 203 - In every triangle the sum of the three angles is equal to two right angles.
Σελίδα 162 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Σελίδα 141 - If a pyramid is cut by a plane parallel to its base, the...