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Elements of Geometry Upon the Inductive Method; To Which Is Added an Introduction to Descriptive Geometry
Elements of Geometry Upon the Inductive Method To Which Is Added an Introduction to Descriptive Geometry Author:James Hayward General Books publication date: 2009 Original publication date: 1829 Original Publisher: Hilliard and Brown Subjects: Geometry Geometry, Descriptive History / General Juvenile Nonfiction / Mathematics / Geometry Mathematics / Geometry / General Notes: This is a black and white OCR reprint of the original. It has no illustrations ... more »and there may be typos or missing text. When you buy the General Books edition of this book you get free trial access to Million-Books.com where you can select from more than a million books for free. Excerpt: PART FIRST. Section II. -- Of the Measure and Comparison of Plane Surfaces. 149. In discussing the properties of plane figures thus far, we have considered only the lines and the angles, and their several relations to each other, without regarding the quantity of surface embraced by the outline or perimeter of the figure. The whole amount of surface or superficies in any geometrical figure is called its area. The word surface, in general, we use to signify superficial extent without regard to quantity. 150. In speaking of figures as equal, we have said that it is an indispensable condition of geometrical equality that the figures compared should coincide by superposition. But it is evident that two figures may have the same amount of surface, and still be very different in form. Such figures we call equivalent. A field of a circular form may have the same superficial extent with another field whose form is quadrangular ; we should say that the two fields are equivalent or equal in area.. In comparing parallelograms we consider one side as the base of the figure, and the perpendicular distance of this side from the opposite, the height of the figure. Sometimes we call one side the inferior base, and the opposite, the superior base. In triangles one side is taken for the base, and the perpendicular distance of this side from the vertex of the opposite angle, is the height of the triangle. 151. To compare two parallelogr...« less