A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration, Containing Many Valuable Discoveries and Impovements in Mathematical Science ...: Designed as a Text Book for Collegiate and Academic Instruction, and as a Practical Compendium on MensurationCollins brothers & Company, 1845 |
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Página 8
... parallel planes , which form its bases . One of those planes may be tangent to the sphere ; in which case , the zone has only a single base . 13. A spherical segment is the portion of the solid sphere included between two parallel ...
... parallel planes , which form its bases . One of those planes may be tangent to the sphere ; in which case , the zone has only a single base . 13. A spherical segment is the portion of the solid sphere included between two parallel ...
Página 12
... parallel to it . Let ED be perpendi- cular to the great_circle AMB ; then will E and D be its poles ; as also the poles of the parallel small circles HPP , FNG . For , DC being perpen- dicular to the plane AMB , A is perpendicular to ...
... parallel to it . Let ED be perpendi- cular to the great_circle AMB ; then will E and D be its poles ; as also the poles of the parallel small circles HPP , FNG . For , DC being perpen- dicular to the plane AMB , A is perpendicular to ...
Página 167
... parallel thereto , and CH will be the value of a required . In like manner , if the base and the difference of the hypothenuse M- and perpendicular be given , we B E N C F H shall have by putting d for the difference and the other ...
... parallel thereto , and CH will be the value of a required . In like manner , if the base and the difference of the hypothenuse M- and perpendicular be given , we B E N C F H shall have by putting d for the difference and the other ...
Página 168
... parallel to HI , we shall have : EF EG FI : GB : : EI : EB : : II : AB consequently , EF : EG :: HI : AB x :: b : AB , - bx - Or , a : a - ab whence AB = But , AB GF α = x , ab - therefore , and Or , a bx ab bx = ax — ab = ax + bx = = x ...
... parallel to HI , we shall have : EF EG FI : GB : : EI : EB : : II : AB consequently , EF : EG :: HI : AB x :: b : AB , - bx - Or , a : a - ab whence AB = But , AB GF α = x , ab - therefore , and Or , a bx ab bx = ax — ab = ax + bx = = x ...
Página 190
... parallel to Tt and cutting PW in v . Through S draw RS parallel to Tt . Let QZ , a tangent at Q , cut WP , produced in Z. Z Then Qq is an ordinate to the di- ameter PW ; Rr is the parameter of PW . W Pv is the abscissa of PW ...
... parallel to Tt and cutting PW in v . Through S draw RS parallel to Tt . Let QZ , a tangent at Q , cut WP , produced in Z. Z Then Qq is an ordinate to the di- ameter PW ; Rr is the parameter of PW . W Pv is the abscissa of PW ...
Otras ediciones - Ver todas
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... Nathan Scholfield Sin vista previa disponible - 2018 |
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... Nathan Scholfield Sin vista previa disponible - 2018 |
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... Nathan Scholfield Sin vista previa disponible - 2018 |
Términos y frases comunes
abscissa altitude arithmetical progression axes base bisected chord circle circular circular segment circumference cone conjugate axis construction convex surface corresponding cosec cosine cylinder described diameter distance divided draw drawn ellipse equal to half equation expression feet find the solidity formed formula Geom geometrical given height hence hyperbola inches infinite series latus rectum length logarithm major axis middle frustum minor axis multiplied ordinate parabola paraboloid parallel parallelogram perpendicular plane portion prism PROBLEM Prop PROPOSITION pyramid quadrant quantity radii radius ratio rectangle revoloidal surface right angles Scholium sector segment sides similar similar triangles sine specific gravity sphere spherical triangle spheroid spindle square straight line tangent THEOREM tion transverse axis Trigonometry ungula versed sine vertex vertical virtual centre zone
Pasajes populares
Página 44 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Página 197 - ... is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16. And this point is called the centre of the circle.
Página 81 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 219 - To find the solidity of a hyperbolic conoid, or otherwise called a hyperboloid. RULE. To the square of the radius of the base, add the square of the diameter...
Página 68 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
Página 14 - ... this point of intersection, as a pole, and limited by the sides, produced if necessary. Let the angle BAC be formed by the two arcs AB, AC ; then it will be equal to the angle FAG formed by the tangents AF, AG, and be measured by the arc DE, described about A as a pole.
Página 27 - The circumference of every circle is supposed to be divided into 360 equal parts...
Página 36 - The solidity of a cylinder is equal to the area of its base multiplied by its altitude.
Página 7 - The radius of a sphere is a straight line, drawn from the centre to any point of the surface ; the diameter, or axis, is a line passing through this centre, and terminated on both sides by the surface.