A Treatise on Elementary Geometry: With Appendices Containing a Collection of Exercises for Students and an Introduction to Modern GeometryJ.B. Lippincott, 1872 - 368 σελίδες |
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Σελίδα 52
... chord is any straight line joining two points of the circum- ference ; as DF . The arc DEF is said to be subtended by its chord DF . Every chord subtends two arcs , which together make up the whole circumference . Thus DF subtends both ...
... chord is any straight line joining two points of the circum- ference ; as DF . The arc DEF is said to be subtended by its chord DF . Every chord subtends two arcs , which together make up the whole circumference . Thus DF subtends both ...
Σελίδα 53
... chord . A sector is the space included between an arc and the two radii drawn to its extremities ; as AOB . 3. From ... CHORDS . PROPOSITION I. - THEOREM . 6. A straight line cannot intersect a circumference in more than two points . For ...
... chord . A sector is the space included between an arc and the two radii drawn to its extremities ; as AOB . 3. From ... CHORDS . PROPOSITION I. - THEOREM . 6. A straight line cannot intersect a circumference in more than two points . For ...
Σελίδα 54
... chord . Let AC be any Ichord which is not a diame- ter , and AOB a diameter drawn through A : then AB > AC . For , join OC . Then , AO + OC > AC ( I. 66 ) ; that is , since all the radii are equal , AO + OB > AC , or AB > AC . B ...
... chord . Let AC be any Ichord which is not a diame- ter , and AOB a diameter drawn through A : then AB > AC . For , join OC . Then , AO + OC > AC ( I. 66 ) ; that is , since all the radii are equal , AO + OB > AC , or AB > AC . B ...
Σελίδα 55
... chords , and conversely . Let O , O ' , be the centres of equal circles , and AB , A'B ' , equal arcs ; then , the ... chord , and conversely ; the arcs being both less than a semi - circumference . Let the arc AC be greater than the ...
... chords , and conversely . Let O , O ' , be the centres of equal circles , and AB , A'B ' , equal arcs ; then , the ... chord , and conversely ; the arcs being both less than a semi - circumference . Let the arc AC be greater than the ...
Σελίδα 56
... chord AC is greater than the chord AB . M M B For , draw the radii OA , OB , OC . In the triangles AOC , AOB , the angle AOC is obviously greater than the angle AOB ; therefore , ( I. 84 ) , chord AC chord AB . Conversely , if chord AC ...
... chord AC is greater than the chord AB . M M B For , draw the radii OA , OB , OC . In the triangles AOC , AOB , the angle AOC is obviously greater than the angle AOB ; therefore , ( I. 84 ) , chord AC chord AB . Conversely , if chord AC ...
Άλλες εκδόσεις - Προβολή όλων
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... William Chauvenet Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... William Chauvenet Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC² adjacent angles altitude apothem base bisects centre of similitude chord circumference circumscribed coincide common cone Corollary cylinder Definition denote diagonals diameter dicular diedral angle distance divided draw edges equally distant equilateral equivalent exterior angle faces figure find the locus frustum given circles given plane given point given straight line hence homologous hypotenuse indefinitely inscribed angle isosceles Let ABC measure medial lines middle point number of sides one-half opposite sides parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN plane passed polar pole polyedral angle polyedron prism PROPOSITION pyramid quadrilateral radical axis radii radius rectangle regular polygon respectively right angles right triangle Scholium secant segment similar sphere spherical polygon square straight line drawn straight line joining surface symmetrical tangent tetraedron theorem three given triangle ABC triedral vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 128 - The area of a rectangle is equal to the product of its base and altitude.
Σελίδα 348 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Σελίδα 19 - The perpendicular is the shortest line that can be drawn from a point to a straight line.
Σελίδα 79 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Σελίδα 29 - The sum of the three angles of any triangle is equal to two right angles.
Σελίδα 175 - If a straight line is perpendicular to each of two straight lines at' their point of intersection, it is perpendicular to the plane of those lines.
Σελίδα 263 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Σελίδα 219 - A truncated triangular prism is equivalent to the sum of three pyramids, whose common base is the base of the prism and whose vertices are the three vertices of the inclined section.
Σελίδα 197 - A right prism is a prism •whose lateral edges are perpendicular to the planes of the bases.
Σελίδα 127 - Any two rectangles are to each other as the products of their bases by their altitudes. Let R and R...