Plane and solid geometry PDF
Preview Plane and solid geometry
, , A 1003 911 BLAINE NEWMAN Ks . House PAL A UW 1817 ENDRIULUI DOULUNAN ARTES SCIENTIA LIBRARY VERITAS U D MIVERSITITYYOOFFMICHIA UL T MICHIGAN U T CULLVON N A R U S N TUEBOR I T U N N LI -SI:QUE-RPEIENSNININS-SUAULMLAAM TAL CIRCUSMPISCPEICE LLLLUTTY CASPPEJUS LLLLMMIN EAST ENGINEERING LLLMINU LIBRARY METRONOMO UNHKTOW I TROSTATAL Am Haltenberger hun Antor East Engla. Library QA 453 : 539 1925 PLANE AND SOLID GEOMETRY THE MACMILLAN COMPANY NEWYORK•BOSTON•CHICAGO•DALLAS ATLANTA•SANFRANCISCO MACMILLAN & CO., LIMITED LONDON· BOMBAY•CALCUTTA MELBOURNE THEMACMILLAN CO. OF CANADA , LTD. TORONTO PLANE AND SOLID GEOMETRY BY ARTHUR SCHULTZE, PH.D. FORMERLY ASSISTANT PROFESSOR OF MATHEMATICS , NEW YORK UNIVERSITY , AND HEAD OF THE MATHEMATICAL DEPART MENT, HIGH SCHOOL OF COMMERCE,NEW YORK CITY AND FRANK . SEVENOAK L FORMERLY PRINCIPAL OF THE ACADEMIC DEPARTMENT STEVENS INSTITUTE OF TECHNOLOGY REVISED BY ELMER SCHUYLER HEAD OF THE DEPARTMENT OF MATHEMATICS BAY RIDGE HIGH SCHOOL, BROOKLYN , NEW YORK ; viss New York THE MACMILLAN COMPANY 1925 All rights reserved PRINTEDIN THEUNITEDSTATESOF AMERICA COPYRIGHT, 1901, 1913,1925, BY THE MACMILLAN COMPANY. Setupandelectrotyped. PublishedMay,192.5 Norwood Press J. S. Cushing Co. —Berwick &Smith Co. Norwood,Mass., U.S.A. 1.Семии. 2-4-43 PREFACE TO THE FIRST EDITION It is generally conceded that the final aim ofmathemati cal teaching should benot only the acquisition ofpractical knowledge but that training of the studen't s mind which givesa distinct gain inmental power. In recognition ofthis principle nearly all college entrance examinations n geometry i require some original work,and most textbooks devote con siderable space to exercises. Comparatively little,however, hasbeen done to introduce the student systematically toorigi nal geometrical work. No teacher of physics or chemistry would ask a student todiscover a law without soguiding his work as to enable him toreach the desired result;many text books and teachers expect the pupil to invent geometrical proofs and to solve problems,entirely new to him,without offering any assistancefurther than aknowledge ofthe well established theorems ofall textbooks. Some writers give a description of the analysis ofpropositions,which is entirely logical and ofgreat advantage toaperson ofsomemathemati calknowledge,butwhich isusually too abstract to be ofany practicalvalue to thebeginner. In this book the attempt is made o introduce the student systematically othe solution t t ofgeometrical exercises. Inthe beginning theexercises given inacertain group are ofsimilar kind and related to the pre ceding proposition; later some general principles are devel oped which are offundamental importance fororiginal work, r as, foexample,the method ofproving the equality oflines bymeans ofequal triangles; themethod ofproving thepro portionality oflines bymeans ofsimilar triangles,etc.;and vi PREFACE TO THE FIRST EDITION finally the analyses oftheorems and problemsare introduced , but in amore concrete form than usual. The propositions are arranged with the view to obtaining a perfect logical and pedagogical order. An unusually large number of exercises is given , selected with care for the pur pose of securing increased mentalpower. The general plan and the preparation of the greater part of the book are the work of Dr. Schultze, while that of Dr. Sevenoak has been chiefly editorial. PREFACE THE FIRST REVISED TO EDITION The main purpose of the revision of this book has been to emphasize still further and to elaborate in greater detail the principalaim of the original edition, viz.,tointroduce the stu dent systematically to original geometric work. Tomake the teaching ofgeometry both disciplinary and informational; to give to the student mental training instead ofteaching him mere facts; to develop his power instead ofmaking him memorize,— these are the fundamental aims ofthis book. Themeans employed for this purpose are similar tothose used inthe first edition. Still greateremphasis,howeve,r has been placed upon the generalmethods which may beused for the solution oforiginal exercises. The grading and theselec tion ofexercises have been carefully revised. All originals that appeared unfit or too difficult have been eliminated or y replaced bsimpler and better ones. Topics offundamental importance,e.g.themethods ofdemonstrating the equality oflines,are represented n greater detail and illustrated by i a greater number ofexercises than in the first edition. In addition tothese fundamental tendencies,a number of minor improvements have been introduced, among which may bementioned:
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