Elements of Geometry: With Practical Applications, for the Use of SchoolsRichardson, Lord & Holbrook, 1829 - 129 páginas |
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Página 32
... remain a right angle L M C. Hence E F is perpendic- ular to C D , which was the first thing to be demonstra- ted . 2. The second part hardly needs demonstration , but it can be demonstrated as follows . If A B and C D are perpendicular ...
... remain a right angle L M C. Hence E F is perpendic- ular to C D , which was the first thing to be demonstra- ted . 2. The second part hardly needs demonstration , but it can be demonstrated as follows . If A B and C D are perpendicular ...
Página 34
... remain after taking from the equal semicircumferences HMI and H O I , the equal arcs HM and H O. Lastly , if both the parallels were tangents , the arcs in question would be semicircumfer- ences , and therefore equal . 41. THEOREM ...
... remain after taking from the equal semicircumferences HMI and H O I , the equal arcs HM and H O. Lastly , if both the parallels were tangents , the arcs in question would be semicircumfer- ences , and therefore equal . 41. THEOREM ...
Página 35
... remains , then , to prove that D G half of B GA the intercepted arc . Now if D G be taken from B G A , we have remaining B D + A G. But B D + A G = F E , since B D A E ( 40 ) , A G = A F , and A E + A F = F E. Moreover F E = D G , since ...
... remains , then , to prove that D G half of B GA the intercepted arc . Now if D G be taken from B G A , we have remaining B D + A G. But B D + A G = F E , since B D A E ( 40 ) , A G = A F , and A E + A F = F E. Moreover F E = D G , since ...
Página 37
... remain . Also if A + B be taken from 180 ° , B C A will remain . Now those things which , when taken from the same thing , leave equal remainders , must themselves be equal . Therefore B C D = A + B . 50. THEOREM . - If a triangle is ...
... remain . Also if A + B be taken from 180 ° , B C A will remain . Now those things which , when taken from the same thing , leave equal remainders , must themselves be equal . Therefore B C D = A + B . 50. THEOREM . - If a triangle is ...
Página 40
... remain- ing side , make another arc cutting the first . draw D E and F E , and the triangle is construct- ed ; since , by the preceding proposition , no triangle having the same things given , can differ from the one in question . 59 ...
... remain- ing side , make another arc cutting the first . draw D E and F E , and the triangle is construct- ed ; since , by the preceding proposition , no triangle having the same things given , can differ from the one in question . 59 ...
Otras ediciones - Ver todas
Elements of Geometry: With Practical Applications, for the Use of Schools Timothy Walker Sin vista previa disponible - 2023 |
Elements of Geometry: With Practical Applications, for the Use of Schools Timothy Walker Sin vista previa disponible - 2019 |
Términos y frases comunes
A B C D A B fig adjacent angles angles are equal axis B A C base and altitude base multiplied bisect called centre chord circ circumference coincide contain convex surface cube cylinder definition demonstrated diameter divided draw equally distant equivalent found by multiplying frustum geometry given line given square greater half the arc Hence homologous sides hypothenuse inches infinite number infinitely small inscribed angles inscribed circle line A B line drawn linear unit mean proportional number of sides parallel sides parallelopiped perim perpendicular polyedrons preceding proposition proved pyramid radii radius regular polygon right angles right parallelogram right triangle semicircumference similar triangles solid angles sphere square feet straight line suppose tangent THEOREM.-The solidity tion trapezoid triangle A B C triangles are equal triangular prism vertex vertices
Pasajes populares
Página ii - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...
Página 48 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Página 63 - The square described on the hypotenuse of a right triangle is equivalent to the sum of the squares on the other two sides.
Página ii - ... and also to an Act, entitled, " An Act- supplementary to an Act, entitled, ' An Act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies, during the limes therein mentioned ;' and extending the benefits thereof to the arts of designing, engraving, and etching historical, and other prints.
Página xiv - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Página xv - LET it be granted that a straight line may be drawn from any one point to any other point.
Página 41 - In any proportion, the product of the means is equal to the product of the extremes.
Página xiv - Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another.
Página 42 - Multiplying or dividing both the numerator and denominator of a fraction by the same number does not change the value of the fraction.
Página xiv - Things which are halves of the same are equal to one another. 8. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. Two straight lines cannot enclose a space. 11. All right angles are equal to one another.