The elements of geometry, in eight books; or, First step in applied logic1874 |
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Σελίδα xviii
... Centre Angles • V. On the Measurement of Angles PAGE • 131 • 145 · 150 158 · 166 CHAPTER II . ON PROPORTIONAL LINES . SECTION I. On Straight Lines cut by Parallels . II . On Straight Lines in the Circumference PROBLEMS BOOK III . ON ...
... Centre Angles • V. On the Measurement of Angles PAGE • 131 • 145 · 150 158 · 166 CHAPTER II . ON PROPORTIONAL LINES . SECTION I. On Straight Lines cut by Parallels . II . On Straight Lines in the Circumference PROBLEMS BOOK III . ON ...
Σελίδα 76
... centre . It is evident that if a straight line , the extremities of which are within the circumference , be ... centre ; some- times it is designated by letters at some of its points , and sometimes by the letter at the centre , together ...
... centre . It is evident that if a straight line , the extremities of which are within the circumference , be ... centre ; some- times it is designated by letters at some of its points , and sometimes by the letter at the centre , together ...
Σελίδα 77
... centre , and that its middle point is the centre of the circumference ; also that all diameters of a circumference are equal to one another . 1 When one of two unequal arcs formed by the same chord in the same circumference is ...
... centre , and that its middle point is the centre of the circumference ; also that all diameters of a circumference are equal to one another . 1 When one of two unequal arcs formed by the same chord in the same circumference is ...
Σελίδα 78
... centre C be joined to the extremities of the chord and to any point D of the chord be- tween A and B ; then C A and CB are two radii [ Def . 24 ] . Because C A and C B are equal to each other [ Def . 23 ] , the line CD is shorter than ...
... centre C be joined to the extremities of the chord and to any point D of the chord be- tween A and B ; then C A and CB are two radii [ Def . 24 ] . Because C A and C B are equal to each other [ Def . 23 ] , the line CD is shorter than ...
Σελίδα 79
... centres C and O are not distinct points , but one and the same centre : therefore the circumference ABD has only one centre , W. W. T. B. D. D B COROLLARY I. Two equal circumferences which coincide through- out , have the same centre ...
... centres C and O are not distinct points , but one and the same centre : therefore the circumference ABD has only one centre , W. W. T. B. D. D B COROLLARY I. Two equal circumferences which coincide through- out , have the same centre ...
Συχνά εμφανιζόμενοι όροι και φράσεις
A B and C D A B C and D E F adjacent angles adjacent sides altitude angle A B C angle ABC angles formed apothem bisect bisectrix centre angle centre line chord circular segment coincide Const Conversely COROLLARY II diagonals diameter divided equal angles equal circumferences equal to half equally distant equilateral equilateral polygon equivalent Eucl extremities given straight line greater homologous hypothenuse inscribed angle intercepts intersection isosceles trapezium isosceles triangle Let A B C magnitude middle line middle perpendicular middle point parallel parallelogram perimeter plane figure point H point of tangence points of section portions produced quadrangle quantities radii radius reasoning would prove rectangle regular polygon right-angled triangle Scholium segment sides A B square straight angle symmetric points tangent THEOREM transversal trapezium triangle A B C unequal vertex W. W. T. B. D. COROLLARY W. W. T. B. D. Inversely
Δημοφιλή αποσπάσματα
Σελίδα 226 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Σελίδα 202 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 230 - 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 143 - When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of the angles is called a, right angle ; and the straight line which stands on the other is called a perpendicular to it. 11. An obtuse angle is that which is greater than a right angle. 12. An acute angle is that which is less than a right angle. 13. A term or boundary is the extremity of any thing.
Σελίδα 218 - 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 202 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Σελίδα 268 - 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 43 - The projection of a point on a plane is the foot of the perpendicular drawn from the point to the plane.
Σελίδα 335 - Assuming that the areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles...
Σελίδα 382 - FLC, there -are two angles -of the one equal to two angles of the other, each to each ; and the side FC which is adjacent to the equal...