Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement on the Quadrature of the Circle and the Geometry of Solids ...J. Eastburn & Company, 1819 - 317 σελίδες |
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Σελίδα xiii
... cosines of arches , which are the founda- tion of those applications of Trigonometry lately in- troduced , with so much advantage , into the higher Geometry . In the Spherical Trigonometry , the rules for pre- venting the ambiguity of ...
... cosines of arches , which are the founda- tion of those applications of Trigonometry lately in- troduced , with so much advantage , into the higher Geometry . In the Spherical Trigonometry , the rules for pre- venting the ambiguity of ...
Σελίδα 225
... Cosine , Cotangent , or Cosecant of that angle . Thus , let CL or DB , which is equal to CL , be the sine of the angle CBH ; HK the tangent , and BK the secant of the same angle ; CL or BD is the co- sine , HK the cotangent , and BK the ...
... Cosine , Cotangent , or Cosecant of that angle . Thus , let CL or DB , which is equal to CL , be the sine of the angle CBH ; HK the tangent , and BK the secant of the same angle ; CL or BD is the co- sine , HK the cotangent , and BK the ...
Σελίδα 227
... cosine of AC , and EH of AB , the sum of these cosines , and KB their difference ; for FK = EL EH + EL , and KB = LH = EH - EL . FDK : tan . BDK ; and tan . FDK = cotan . DFK , because DFK is the complement of FDK ; therefore , FK : KB ...
... cosine of AC , and EH of AB , the sum of these cosines , and KB their difference ; for FK = EL EH + EL , and KB = LH = EH - EL . FDK : tan . BDK ; and tan . FDK = cotan . DFK , because DFK is the complement of FDK ; therefore , FK : KB ...
Σελίδα 230
... cosine of the angle included by the two sides . Let ABC be any triangle , 2AB.BC is to the difference between AB2 + BC2 and AC2 as radius to cos . B. From A draw AD perpendicular to BC , and ( 12. and 13. 2. ) the difference between the ...
... cosine of the angle included by the two sides . Let ABC be any triangle , 2AB.BC is to the difference between AB2 + BC2 and AC2 as radius to cos . B. From A draw AD perpendicular to BC , and ( 12. and 13. 2. ) the difference between the ...
Σελίδα 231
... cosine of half the angle included between the two sides of the triangle . Let ABC be a triangle , of which BC is the base , and AB the great- er of the other two sides , 4AB.AC : ( AB + AC + BC ) ( AB + AC — BC ) :: R3 ( cos . BAC ) 2 ...
... cosine of half the angle included between the two sides of the triangle . Let ABC be a triangle , of which BC is the base , and AB the great- er of the other two sides , 4AB.AC : ( AB + AC + BC ) ( AB + AC — BC ) :: R3 ( cos . BAC ) 2 ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference common section cosine cylinder demonstrated diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 153 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle...
Σελίδα 19 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Σελίδα 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.
Σελίδα 292 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 308 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Σελίδα 18 - 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.
Σελίδα 78 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.
Σελίδα 77 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Σελίδα 39 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the too interior angles upon the same side together equal to two right angles.
Πληροφορίες βιβλιογραφίας
| Τίτλος | Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement on the Quadrature of the Circle and the Geometry of Solids ... |
| Συγγραφέας | John Playfair |
| Εκδότης | J. Eastburn & Company, 1819 |
| Πρωτότυπο από | η Δημόσια Βιβλιοθήκη της Νέας Υόρκης |
| Ψηφιοποιήθηκε στις | 21 Ιουν. 2006 |
| Μέγεθος | 317 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |