Elements of Geometry and Trigonometry: From the Works of A.M. LegendreA.S. Barnes, 1874 - 455 páginas |
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Página 18
... given points . 12. The shortest distance from one point to another is measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line . POSTULATES . 1 ...
... given points . 12. The shortest distance from one point to another is measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line . POSTULATES . 1 ...
Página 19
... given straight line an angle equal to a given angle . 8. A straight line may be drawn through a given point , parallel to a given line . NOTE . In making references , the following abbreviations are employed , viz . › A. for Axiom ; B ...
... given straight line an angle equal to a given angle . 8. A straight line may be drawn through a given point , parallel to a given line . NOTE . In making references , the following abbreviations are employed , viz . › A. for Axiom ; B ...
Página 23
... given angles ( A. 9 ) . Hence , the sum of the given angles is equal to four right angles . PROPOSITION III . THEOREM . If two straight lines have two points in common , they will coincide throughout their whole extent , and form one ...
... given angles ( A. 9 ) . Hence , the sum of the given angles is equal to four right angles . PROPOSITION III . THEOREM . If two straight lines have two points in common , they will coincide throughout their whole extent , and form one ...
Página 33
... given point only one perpendicular can be drawn to a given straight line . Let A be a given point , and AB a perpendicular to DE : then can no other perpendicular to DE be drawn from A. A D- BE F For , suppose a second perpendicular AC ...
... given point only one perpendicular can be drawn to a given straight line . Let A be a given point , and AB a perpendicular to DE : then can no other perpendicular to DE be drawn from A. A D- BE F For , suppose a second perpendicular AC ...
Página 34
... given line at points equally distant from the foot of the perpendicular , will be equal : 3 ° . Of two oblique lines that meet the given line at points unequally distant from the foot of the perpendicular , the one which meets it at the ...
... given line at points equally distant from the foot of the perpendicular , will be equal : 3 ° . Of two oblique lines that meet the given line at points unequally distant from the foot of the perpendicular , the one which meets it at the ...
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Términos y frases comunes
AB² ABCD AC² adjacent angles altitude apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine slant height sphere spherical polygon spherical triangle square subtracted Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence
Pasajes populares
Página 126 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Página 59 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Página 18 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Página 104 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Página 6 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 28 - If two triangles have two sides of the one equal to two sides of the...
Página 46 - 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.
Página 99 - The area of a parallelogram is equal to the product of its base and altitude.
Página 172 - If two planes are perpendicular to 'each other, a straight line drawn in one of them, perpendicular to their intersection, will be perpendicular to the other.
Página 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.