An Account and Description of Capt. W. Mugford's Temporary Rudder, and for Which the Extra-Magellanic Premium Was Awarded
William Mugford
1809
Transactions of the American Philosophical Society
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... ntent at http://about.jstor.org/participate--jstor/individuals/early-journal--content. JSTOR is a digital library of academic journals, books, and primary source objects. JSTOR helps people discover, use, and build upon a wide range of content through a powerful research and teaching platform, and preserves this content for future generations. JSTOR is part of ITHAKA, a not--for--profit organization that also includes Ithaka S+R and Portico. For more information about JSTOR, please contact support@jstor.org. DEMONSTRATED. DEMONSTRATED. angles GZH, HPK, have equal angles, GZH and HPK, because GZ is parallel to HP and ZH to KW, and the sides ZH, ZG, KP, PH which are about the equal angles proportional, therefore the remaining angles HGZ, GHZ of the triangle GZH are equal to the remaining angles PHK, PKH of the triangle HPK, each to each which are opposite to the homologous sides, so the angle HGZ is equal to the angle PHK and the angle GHZ is equal to the angle PKH. The angle ZHP is equal to the angle HPK, because ZH is parallel to PK and P1I falls upon them; and the three angles GHZ, ZHP, and PHK taken together are equal to the three angles HKP, HPK, and PHK taken together, that is to two right angles. So to the point H in the right line ZH are drawn two right lines KH and GH on opposite sides, making the two angles KHZ and GHZ taken together equal to two right angles; therefore the two right lines form one straight line; But BC is bisected in K by construction, and the right line GHK drawn througll G and 11 bisects BC. Therefore in the triangle ABC, CD and BE being drawn, cutting each other in F, and the sides of tlhe triangle in D and E, and the diagonals AF DE of the trapezium ADFE being drawn and bisected in G and H, the right line GH joining the points of bisection being produced bisect the base. Q. E. D. _
doi:10.2307/1004792
fatcat:6rqaqtavcfamvom76kk5ao2dlu