О доказательстве в геометрии: Выпуск 14 (Russian Edition)

Odnazhdy, v samom nachale uchebnogo goda, mne prishlos' uslyshat' razgovor dvuh devochek. Starshaya iz nih pereshla v shestoj klass, mladshaya - v pyatyj. Devochki delilis' svoimi vpechatleniyami ob urokah, uchitelyah, podrugah, o novyh predmetah. Shestiklassnitsu ochen' udivili uroki geometrii: "Vot chudesa, - govorila ona, - prishla uchitel'nitsa v klass, narisovala na doske dva ravnyh treugol'nika, a potom tselyj urok dokazyvala nam, chto oni- ravnye. Nikak ne pojmu: zachem eto nuzhno?". - "A kak zhe ty urok budesh' otvechat'?"- sprosila mladshaya devochka. -"Vyuchu po uchebniku... vot tol'ko ochen' trudno zapomnit', gde kakuyu bukvu nuzhno stavit'.,.". V tot zhe den' vecherom ya slyshal, kak eta devochka, sidya u okna, userdno uchila geometriyu: "Dlya dokazatel'stva nalozhim treugol'nik A'V'S' na treugol'nik AVS... nalozhim treugol'nik A'V'S' na treugol'nik ABC.." - neodnokratno povtoryala ona. K sozhaleniyu, mne ne udalos' uznat', naskol'ko uspeshno uchilas' eta devochka po geometrii, no dumaetsya, chto uchit'sya ej po etomu predmetu bylo dovol'no trudno. Neskol'ko dnej spustya prishel ko mne moj sosed po kvartire Tolya, tozhe shestiklassnik" i takzhe s pretenziyami k geometrii. Im rasskazali na uroke i zadali na dom vyuchit' teoremu o tom, chto v treugol'nike vneshnij ugol bol'she vsyakogo vnutrennego, ne smezhnogo s nim. Tolya pokazal mne chertezh iz uchebnika Kiseleva (chert. 1) i sprosil: "Zachem nuzhno privodit' dlinnoe i slozhnoe dokazatel'stvo, kogda na etom chertezhe sovershenno yasno vidno, chto vneshnij ugol treugol'nika - tupoj, a ne smezhnye s nim vnutrennie ugly - ostrye? No ved' tupoj ugol vsegda bol'she ostrogo,-ubezhdal menya Tolya,-eto zhe yasno bez vsyakogo dokazatel'stva". I mne prishlos' raz'yasnit' Tole, chto predlozhenie eto sovsem ne ochevidno i chto esli polnoe osnovanie trebovat' dokazatel'stva predlozheniya o vneshnem ugle treugol'nika. This book, "O dokazatel'stve v geometrii Vypusk 14", by A. I. Fetisov, is a replication of a book originally published before 1954. It has been restored by human beings, page by page, so that you may enjoy it in a form as close to the original as possible.