Elements of Plane and Solid Geometry: And of Plane and Spherical Trigonometry ; to which is Added Mensuration, Surveying, and NavigationHarper, 1867 - 283 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 36.
Σελίδα 11
... . Consequently , a semicircle , or 180 degrees , is the measure of two right angles ; and a quadrant , or 90 degrees , the measure of one right angle . THEOREM VII . When two lines intersect each other , THEOREMS . 11.
... . Consequently , a semicircle , or 180 degrees , is the measure of two right angles ; and a quadrant , or 90 degrees , the measure of one right angle . THEOREM VII . When two lines intersect each other , THEOREMS . 11.
Σελίδα 12
... intersect each other , the opposite angles are equal . Let the two lines AB , CD , intersect in the point E ; then will the angle AEC be equal to the angle BED , and the angle AED be equal to the angle A CEB . E D For , since the line ...
... intersect each other , the opposite angles are equal . Let the two lines AB , CD , intersect in the point E ; then will the angle AEC be equal to the angle BED , and the angle AED be equal to the angle A CEB . E D For , since the line ...
Σελίδα 32
... intersect each other in E ; then will AE be equal to EC , and BE to ED ; and the sum of the squares of AC , BD , will be equal to the sum of the squares of AB , BC , CD , DA . That is , AE and B EC , and BE - ED , AC2 + BD - AB2 + BC2 + ...
... intersect each other in E ; then will AE be equal to EC , and BE to ED ; and the sum of the squares of AC , BD , will be equal to the sum of the squares of AB , BC , CD , DA . That is , AE and B EC , and BE - ED , AC2 + BD - AB2 + BC2 + ...
Σελίδα 33
... or the parallelogram be a rhombus , then AD - AE2 + ED , CD2 - DE2 + CE2 , & c . Cor . 2. Hence , and by th . 34 , the diagonals of a rhombus intersect at right angles . B 2 BOOK II . OF THE CIRCLE . THEOREM I. If THEOREMS . 33.
... or the parallelogram be a rhombus , then AD - AE2 + ED , CD2 - DE2 + CE2 , & c . Cor . 2. Hence , and by th . 34 , the diagonals of a rhombus intersect at right angles . B 2 BOOK II . OF THE CIRCLE . THEOREM I. If THEOREMS . 33.
Σελίδα 43
... intersection of two chords is measured by half the sum of the two intercepted arcs . Let the two chords AB , CD intersect at the point E ; then the angle AEC or DEB is measured by half the sum of the two arcs AC , DB . D A E C Draw the ...
... intersection of two chords is measured by half the sum of the two intercepted arcs . Let the two chords AB , CD intersect at the point E ; then the angle AEC or DEB is measured by half the sum of the two arcs AC , DB . D A E C Draw the ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Plane and Solid Geometry, and of Plane and Spherical Trigonometry Gerardus Beekman Docharty Περιορισμένη προεπισκόπηση - 2022 |
Elements of Plane and Solid Geometry, and of Plane and Spherical Trigonometry Gerardus Beekman Docharty Περιορισμένη προεπισκόπηση - 2022 |
Elements of Plane and Solid Geometry, and of Plane and Spherical ... Gerardus Beekman Docharty Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent allel altitude angles equal bisect centre chord circle circumference cone consequently convex surface cosec cosine cylinder departure diameter diff difference of latitude divided draw drawn equal angles equal th equation equiangular equilateral exterior angle feet figure find the area following RULE formula frustum Geom given angle given line Hence included angle inscribed intersection join latitude Let ABC logarithms longitude measured by half Multiply opposite angles parallel parallelogram perpen perpendicular plane XZ polygon prism Prob PROBLEM produced Prop proportional PROPOSITION pyramid Q. E. D. Corol Q. E. D. THEOREM quadrant quantities radii radius ratio rectangle regular polygon right angles right-angled triangle segment semicircle side BC sine slant height solid angle sphere spherical angle spherical triangle SPHERICAL TRIGONOMETRY square straight line tangent trian triangle ABC versin
Δημοφιλή αποσπάσματα
Σελίδα 15 - THE Angle formed by a Tangent to a Circle, and a Chord drawn from the Point of Contact, is Equal to the Angle in the Alternate Segment.
Σελίδα 2 - If a straight line be divided into any two parts, the square on the whole line is...
Σελίδα 40 - The areas or spaces of circles are to each other as the squares of their diameters or of their radii.
Σελίδα 83 - A cone is a solid figure described by the revolution of a rightangled triangle about one of the sides containing the right angle, which side remains fixed.
Σελίδα 67 - angle in a segment' is the angle contained by two straight lines drawn from any point in the circumference of the segment, to the extremities of the straight line which is the base of the segment.
Σελίδα 1 - When a line is mentioned simply, it means a Right Line. 7. A Curve continually changes its direction between its extreme points. 8. Lines are either Parallel, Oblique, Perpendicular, or Tangential. 9. Parallel Lines are always at the same perpendicular distance; and they never meet though ever so far produced. 10. Oblique lines change their distance, and would meet, if produced on the side of the Jeast distance.
Σελίδα 24 - Proportion, when the ratio is the same between every two adjacent terms, viz. when the first is to the second, as the second to the third, as the third to the fourth, as the fourth to the fifth, and so on, all in the same common ratio.
Σελίδα 25 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.