摘要
《大测》是第一部传入我国的西方三角学著作,其"三要法"、"二简法"和"四根法"中的所表示的三角公式,备受数学史家关注,但是各家对要法三、根法二表述不一.《大测》中"要法三"并非半角公式sin2α=1-cosα2,"根法二"也非余弦定理c2=a2+b2-2abcosC,而"根法三",即正切定理,以ssiinnAA-+ssiinnBB=tan((A+B)/2)tan((A-B)/2)形式给出,与玉山若干(Regiomontanus)在《论各种三角形》中所给出的正切定理形式相同,并非韦达(F.Vi埁te)化简后的等价公式tanA2-B=aa-+bbtanA+2B.由于邓玉函没有给出"简法二"sin(A±B)=sinAcosB±cosAsinB的证明,有人推测其不会证明方法,对此给出了不同意见.
The Dace(大测), written by Jesuit missionary in Jean Terrenz(邓玉函) in Chinese, was the first work introducing western trigonometry. The historians of mathematics paid more attention to the trigonometry formulae in it, especially those entitled san-yao-fa(三要法), er-jian-fa(二简法) and si-gen-fa(四根法). But those formulae were understood differently. This paper proves that the yao-fa-san(要法三) is not sina/2=√1-cosa/2 , the gen-fa-er(根法二 ) nor c^2= a^2 +b^2-2ab cos C , and meanwhile gen-fa-san(根法三) nor sinA+sinB/sinA-sinB=tan((A+B)/2)/tan((A-B)/2) which maybe came from Regiomontanus's De triangulis. It is also doubted that whether Terrenz could prove the formula sin (A ± B) = sin A cos ± cosA sin B , for there appeared no proof in his treatise. The author of the present paper comes to the conclusion that Terrenz knew the proof and considered it as a common.
出处
《内蒙古师范大学学报(自然科学汉文版)》
CAS
2007年第6期677-682,共6页
Journal of Inner Mongolia Normal University(Natural Science Edition)
基金
国家自然科学基金资助项目(10561006)
内蒙古师范大学研究生基金资助项目(YJS06016)
关键词
《大测》
半角公式
余弦定理
正切定理
Dace(大测)
formulae for half-angle
theorem of Cosine
theorem of Tangent