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第704章 一道数学题引发的(上)(2 / 2)

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黄博文用力揉了一会脸。又动用天元术:“吾立天元一为半径,置南行步在地……”

他推算着:“以二行步相乘为实,二行步相并为从,一步常法,得半径。”

刘冬阳也是画图:“余设半径为未知数……”

赵中举又回头做了,李坦然终于算出那鸡的问题。奋起直追。

“今有积以和乘之,减积,余以平乘之加和,得一十七万一百六十二步。只云和为益实。四为益方,三为从上廉,二为益下廉。一为正隅,三平方开之,如平四分之一。问,长,平各几何?”

黄博文答:“平一十二步,长三十步。”

“今有黄方乘直积得二十四步,只云股弦和九步。问勾几何?”

黄博文答:“三步。”

“今有股幂减弦较较与股乘勾等。只云勾幂加弦较和与勾乘弦同。问股几何?”

黄博文立天元一为股,地元一为勾弦和,最后答:“四步。”

他感觉头脑一阵阵眩晕,太阳穴那边,更是阵阵跳着刺痛。刘冬阳也是放下毛笔,稍稍闭目养神,不过黄博文甩了甩头,还是看下一道题:“今有股弦较除弦和与直积等。只云勾股较除弦较和与勾同。问弦几何?”

黄博文极力坐稳,缓缓呼了口气,考试考到现在。能答完这么多题,他深深感到自豪,不过还有永宁侯爷压轴的题目摆在后面,自己一定要做到。

他拿起矩物与铅笔,在草稿上画图:“吾立天元一为勾。地元一为股,人元一为弦,物元一为开数!”

终于,他答完这道题,也终于看到永宁侯王斗,设下的那道压轴大题。

“靖边军有将显才擅使铳,有将瑄擅使炮,显才日射鴽鹅堆积之,叠越大,积越高,瑄笑曰:吾一炮击之,尔鴽堆尽跨也。”

“当知鴽堆为一尖锥,当知诸尖锥有积叠之理,元数起于丝发而递增之,而叠之则成平尖锥。一定之元数叠之则成平方,上少下多之元数叠之则成平尖锥,平方数起于丝发而渐增之而叠之,则成立尖锥。”

“一定之平方叠之则成立方,上少下多之平方叠之则成立尖锥。立方数起于丝发而渐增之变为面,而叠之则成三乘尖锥。当知三乘以上尖锥之底皆方,唯上四面不作平体而成凹形,乘愈多则凹愈甚。”

“当知三乘方数起于丝发而渐增之变为面,而叠之则成四乘尖锥,从此递推至无穷,线,面,体皆有循环之理。”

“请问先生明算者,此尖锥算法何如?尖锥积何多?瑄炮击之,此圆内积何多?”

黄博文目瞪口呆看着,他脑中一片嗡嗡作响,下意识就想:“吾立割圆术,垛积……”

随后又怔住了,割圆术虽可用来无限接近圆面积,称割之弥细,所失弥少,割之又割,以至于不可割,则与圆合体,而无所失矣,然不足解决眼前的问题。

此题有无穷小分割,又有无限大求和,然又定了设定,“当知诸乘方皆有尖锥”、“当知诸尖锥有积叠之理”,然后极限思想中,尖锥似乎又有曲线,又有运动。

还要求赵瑄炮击运动面积,这之间,似乎又是相互活动的。

因为尖锥不断变大变小,炮弹轨迹过去,面积也是不一样的。

这,这如何求积?

各样的画面在脑中转动,黄博文呆呆坐着,让他脑中嗡嗡声更为响动。

“儿啊,考功名才是正途!”

母亲双目中湿润的泪水。

“文儿,你这样下去,可如何是好?”

素来严厉的父亲,已经不说他什么,只是摇摇头,眼中闪过失望的神情,然后转身就走开了。

“黄博文,几十年你还是童生啊?”

同窗轻蔑嘲笑的眼神是如此刺骨,羞辱,打击,历历往事,从眼前飞速闪过。

“不,我要做出这条题,一举成名天下知!”

黄博文挣扎着,他伸手要拿来盘算,然眼前一阵阵金星乱冒,让他坐立不稳。他极力扶着桌面,身子仍不断摇摇晃晃,猛然,他一口鲜血喷出,眼前天旋地转,再也支持不住,就那样摔倒地上。

考房内一片惊叫,赵中举大叫:“不得了,有人考试考得吐血了……”(未完待续。。。)

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