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Loomis’s approach to solving geometry problems through an explicitly analytic method. The material frames why many students fail when attempting original exercises: standard synthetic, deductive textbook procedures do not suffice. Through a set of model solutions and an accompanying discussion of underlying principles, the work aims to teach pupils, students, and teachers how to proceed analytically and analyze concrete conditions effectively.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/original-investigation-how-to-attack-an-exercise-in-geometry-with-many-model-solutions-and-a-complete-discussion-of-the-principles-underlying-the-same/566544/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/original-investigation-how-to-attack-an-exercise-in-geometry-with-many-model-solutions-and-a-complete-discussion-of-the-principles-underlying-the-same/566544.png","ImageObject",300,407,{"name":92,"@type":93},"OmBimo","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-06","2026-10-13",true,{"@type":102,"interactionType":103,"userInteractionCount":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What teaching problem does the preface describe for students tackling original geometry exercises?","Question",{"text":112,"@type":113},"Students often fail to demonstrate success with original geometry exercises because the method learned from texts and teachers is mainly synthetic and deductive, while the method needed for original problems is fundamentally analytic.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the work characterize the method necessary for solving original exercises?",{"text":117,"@type":113},"It emphasizes learning how to proceed analytically and developing the ability to analyze the conditions of concrete questions effectively.",{"name":119,"@type":110,"acceptedAnswer":120},"Who is Elisha S. Loomis according to the document text?",{"text":121,"@type":113},"Elisha Scott Loomis (1852-1940) is presented as a teacher, philosopher, mathematician, educator, author, genealogist, and civil engineer, recognized for his long influence as a teacher.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},566544,1792943566,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":81,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},962090893581,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","# ORIGINAL INVESTIGATION\n\nor  \n# HOW TO ATTACK AN EXERCISEIN GEOMETRY\n\nLoomis  \nBONDED SCALEAND MACHINE COMPANY  \nyA!us W  \n# ORIGINAL INVESTIGATION\n\nor  \n# HOW TO ATTACK AN EXERCISEIN GEOMETRY\n\n## WITH MANY MODEL SOLUTIONS AND A COMPLETEDISCUSSION OF THE PRINCIPLESUNDERLYING THE SAME\n\nBY  \nELISHA S.LOOMIS.Ph.D.  \n1852-1940  \nProfessor of Mathematics,Baldwin University 1885-1895Head of Mathematics Department,West High School,Cleveland,OhioProfessor Emeritus -Baldwin Wallace College  \nEighth printing October 1952Ninth printing June 1954Tenth printing February 1556  \nReprinted and Presented  \nBy  \nTHE BONDED SCALE AND MACHINE COMPANY  \nArthur Gluck,PresidentColumbus,Ohio,U.S.A.  \nManufacturers of:  \nIndustrial scales,crushers,screens,conveyor systems,coalpreparation plants,mineral beneficiation plants.food processing equipmert.  \nIt is the custom of the Bonded Scale and MachineCompany to distribute mathematical and philoso-phical literature to public libraries,college li-braries and educators.This reprinting and freedistribution can only in a small way show appre-ciation for a revered teacher.  \n## Elisha Scott Loomis\n\n1852-1940  \nTEACHER  \nElisha Scott Loomis,philosopher,mathematician,educa-tor,author,genealogist,and civil engineer,prized more thanany thing else the title of Teacher”,for it was in his fiftyyears as a teacher that he exerted the deepest influence on allwho came in contact with him.Not only were thousands offpupils taught by a great mathematician to think things outand prove them”but they received encouragement and inspira-tion from a great man with a keen sense of humor and an in-tensely sympathetic understanding of humanity.  \nBorn in Medina County,Ohio,the eldest of eight children,Elisha Loomis was left fatherless at the age of twelve andwent to work to help support his penniless family.In spite offthe fact that for a long time he was able to attend school foronly a few months each winter,he devoted his life to researchand study.In 1880 he received his B.S.from Baldwin Univers-ity,in 1886 his M.A.,and in 1888 his Ph.D.from Wooster Uni-versity.  \nIn 1885 he became Chairman of the Department of Mathe-matics at Baldwin University succeeding the distinguishedDr.Aaron Schuyler.Because of his liberal views(he used oneof John Dewey's works as a textbook)he left his college po-sition and in 1895 became head of the Mathematics Depart-ment at West High School,Cleveland,Ohio,where he remaineduntil his retirement in 1923.That year the graduating classchose for its motto Not in our stars but in ourselves”--atribute to Dr.Loomis who had chosen that subject for his ora-tion upon his graduation from college.  \nAmong the works of Elisha Scott Loomis were:Theism;The Teaching of Mathematics in High School;Original Investi-gation or How to Attack an Exercise in Geometry;Problemsfrom Algebra and Geometry;Trisection of any Plane Angle;The Loomis Family in America;Life and Appreciation ofAaron Schuyler;and over a hundred articles on educational,mathematical,philosophical,and genealogical subjects.  \nIn 1940 Dr.Loomis published the second edition of thePythagorean Proposition(with 370 proofs)which he consideredhis best work.Dr.H.A.Naber of Baarn,Holland said of Dr.Loomis'investigations on this proposition(translation),Professor Loomis has wrought in his book a work that is moredurable than bron ze and towers higher even than the pyramids.”  \nAnother great mathematician who was familiar with Dr.Loomis'work,Original Investigation or How to Attack an Ex-ercise in Geometry,and who praised it highly was Dr.HenryBlumberg,1888-1950,Professor of Mathematics at Ohio StateUniversity from 1925 to 1950.Like Elisha S.Loomis,he wasa fighter for truth and justice and a true friend.His great workwill probably never be published even though friends wouldhave defrayed the cost.  \nElisha Scott Loomis loved the truth.A righteous man,healways stood up to be counted.He was patient and kind to thepoorest student'(I was one of them)and had a keen understand","cbCaie1itoVDNPrG","https://ap.wps.com/l/cbCaie1itoVDNPrG","pdf",3228358,84,"English","# ORIGINAL INVESTIGATION\n# HOW TO ATTACK AN EXERCISE IN GEOMETRY\n## WITH MANY MODEL SOLUTIONS AND A COMPLETE DISCUSSION OF THE PRINCIPLES UNDERLYING THE SAME\n# Elisha Scott Loomis\n# PREFACE","[{\"question\":\"What teaching problem does the preface describe for students tackling original geometry exercises?\",\"answer\":\"Students often fail to demonstrate success with original geometry exercises because the method learned from texts and teachers is mainly synthetic and deductive, while the method needed for original problems is fundamentally analytic.\"},{\"question\":\"How does the work characterize the method necessary for solving original exercises?\",\"answer\":\"It emphasizes learning how to proceed analytically and developing the ability to analyze the conditions of concrete questions effectively.\"},{\"question\":\"Who is Elisha S. Loomis according to the document text?\",\"answer\":\"Elisha Scott Loomis (1852-1940) is presented as a teacher, philosopher, mathematician, educator, author, genealogist, and civil engineer, recognized for his long influence as a teacher.\"}]","ORIGINAL INVESTIGATION - HOW TO ATTACK AN EXERCISE IN GEOMETRY - WITH MANY MODEL SOLUTIONS AND A COMPLETE DISCUSSION OF THE PRINCIPLES UNDERLYING THE SAME | PDF",1791862762,212]