Companies TEXT-BOOK OF ELEMENTARY PLANE GEOMETRY BY JULIUS PETERSEN, PROFESSOR AT THE ROYAL POLYTECHNIC SCHOOL AT COPENHAGEN TRANSLATED BY R. STEENBERG J R. (AUTHORIZED ENGLISH EDITION) LONDON SAMPSON LOW, MARSTON, SEARLE & RIVINGTON COPENHAGEN: ANDR. FRED. HÖST & SON 1880 (All rights reserved) QA 455 INTRODUCTION. 1. Every object which occurs in nature has numerous properties; to facilitate the investigation of which, one preliminarily endeavours to consider one at a time, independently of the others; the different investigations of the same kind are then collected, and thus the different sciences, natural sciences, are formed. Thus, if we examine a piece of chalk, we might ask about its origin and occurrence, its specific gravity and colour, the combination of its elements, its form, &c., and these questions will be answered respectively by Geology, Physics, Chemistry, and Geometry. 2. Geometry treats of the form without regard to the substance; when we speak of a sphere, we do not consider of what it is made, but only of the space which it occupies; every object occupies a space, which has extension in all directions; this is a geometrical body. The boundary between a body and the surrounding space is called a superficies or the surface of the body; a superficies has no thickness. If a part of a superficies be cut off from the surrounding part, the boundary is called a line; a line has no breadth. If a part of a line be cut off, the limit is termed a point; it has no magnitude, but only denotes position. 3. When a point moves, it produces a line, similarly a superficies may be imagined as being produced through the M513332 |