## Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration. Accompanied with All the Necessary Logarithmic and Trigonometric Tables |

### From inside the book

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**proportions**, we will also refer the student to the method explained in the Algebra . There is this difference between geometrical ratios of magni- tudes , and ratios of numbers : All numbers are commensurable ; that is , their ratio ... Page 48

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**proportions**, since their antecedents are the same , we deduce angle AEG : angle AEK :: arc AH : arc AK , which cannot be , for the antecedent of the first couplet is less than its consequent , while in the second couplet the antecedent ... Page 72

... far as we please , we shall never arrive at a term in which there will be no remainder . Therefore there is no common measure of the diagonal and side of a square . THIRD BOOK . THE

... far as we please , we shall never arrive at a term in which there will be no remainder . Therefore there is no common measure of the diagonal and side of a square . THIRD BOOK . THE

**PROPORTIONS**OF STRAIGHT LINES AND THE 72 GEOMETRY . Page 73

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**PROPORTIONS**OF STRAIGHT LINES AND THE AREAS OF RECTILINEAL FIGURES . DEFINITIONS . I. Two figures are similar when they resemble each other in all their parts , differing only in their comparative magnitudes , so that every point of the ... Page 76

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**proportion**, the product of the extremes is equal to the product of the means , we derive from the above**proportion**, AD : DB :: AE : EC , this equation , ADXEC = DBXAE . Now , in order to comprehend the sense which we 76 GEOMETRY .### Other editions - View all

### Common terms and phrases

a+b+c ACē altitude angles equal apothem bisect centre chord circ circumference cone consequently corresponding cosec Cosine Cotang cylinder decimal denote described diameter dicular distance divided draw drawn equation equivalent exterior angles feet figure formed frustum give given line greater half hence homologous sides hypotenuse inscribed circle intersection logarithm measure middle point multiplied number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right-angled triangle Scholium secant sector similar similar triangles Sine slant height solid sphere spherical triangle square straight line subtract suppose surface Tang tangent THEOREM three sides triangle ABC triangular prism vertex volume