彼得鲁斯·阿皮亚努斯Petrus Apianus

彼得鲁斯·阿皮亚努斯，又名阿皮亚努斯、阿皮亚努斯 Bennewitz和阿皮亚努斯 Bienewitz，是Martin和Gertrud Bienewitz四个儿子之一。他进入莱比锡大学学习数学、天文学和宇宙志。

或许我们应该说明宇宙志研究包含哪些内容。它是一门广泛的科学，旨在为宇宙中一切事物的位置提供数学基础。因此，它要求专门研究这一主题的人成为天文学、地理学、地图制作、航海、测量、建筑、数学仪器和日晷方面的专家。在许多方面，这些可以被视为阿皮亚努斯时代的应用数学学科，我们当然可以把阿皮亚努斯视为一位杰出的应用数学家。阿皮亚努斯在数学及其16世纪的应用方面表现出色，在莱比锡学习后，他搬到维也纳，在那里继续学习同样广泛的应用数学主题。

同样值得注意的是，16世纪初是绘制世界地图的激动人心的时代。Vasco da Gama于1498年从葡萄牙绕过非洲航行到印度。Christopher Columbus于1492年登陆美洲，1522年Ferdinand Magellan在环球航行后返回西班牙。这接近阿皮亚努斯开始出版的时间。他的第一部作品是一幅世界地图Typus orbis universalis，他基于Martin Waldsemüller 1520年的早期作品。阿皮亚努斯的第二部作品在次年问世，这就是IsagogeⓉ（导论），一部关于Typus orbis universalis的地理评论。

1524年，Apain出版了他的第一部重要作品。这就是Cosmographia seu descriptio totius orbis，一部主要基于克劳狄乌斯·托勒密的作品。Cosmographia介绍了天文学、地理学、地图制作、测量、航海、天气与气候、地球形状、地图投影和数学仪器。这本插图丰富的书远不止是一本地图集，但它确实提供了各大洲的草图和一些最早的美洲地图。

1524年出版的Cosmographia取得了一定的成功，但并非真正的畅销书。然而，结合他早期的作品，它显示了阿皮亚努斯的巨大才能，这些出版物是他于1527年被任命为因戈尔施塔特大学数学教授的主要原因。从这时起，他的职业生涯真正起飞，尽管他在那一年出版的算术书并不是主要因素。这部关于算术的小作品的一个方面——像阿皮亚努斯的所有贡献一样，其目标非常实用——是标题页包含了Pascal's triangle。这是这一著名数学内容首次在欧洲印刷出现。

此时，神圣罗马帝国皇帝Charles V作为西班牙国王和奥地利大公统治着欧洲大部分地区，其西班牙和哈布斯堡帝国覆盖了从西班牙和荷兰到奥地利和意大利的欧洲。Charles本人似乎可能在1530年左右在阿皮亚努斯指导下学习过宇宙志，这对如此庞大帝国的统治者来说是一门有用的学科。然而，这方面的证据并不确凿。我们确切知道，到1530年代初，阿皮亚努斯获得了Charles授予的特殊特权，1540年，阿皮亚努斯将他的下一部重要作品Astronomicon Caesareum献给了Charles。

Astronomicon Caesareum 是一部比 Cosmographia 更为宏大的著作。它呈现了许多相同的材料，但方式更为优雅和精炼。它包含了一些重要的新科学思想；例如，阿皮亚努斯 提倡利用日食来确定经度。这本书还描述了五颗彗星，特别是 爱德蒙·哈雷 的彗星，并且在 Astronomicon Caesareum 中，阿皮亚努斯 首次做出了重要观察：彗星的尾巴总是指向远离太阳的方向。Astronomicon Caesareum 令查理五世非常高兴，他因此任命 阿皮亚努斯 为宫廷数学家，并授予 阿皮亚努斯 及其三个兄弟骑士爵位。

在1524年Cosmographia出版和1540年Astronomicon Caesareum出版之间，还有更多重要的出版事件。其中之一是1533年，海马·弗里修斯 出版了 Cosmographia 的新版本。海马·弗里修斯 花费了大量精力编辑和扩充 阿皮亚努斯 的书，这确实得到了回报，因为第二版比第一版更受欢迎，成为整个欧洲的畅销书，被翻译成所有主要欧洲语言。当然，海马·弗里修斯 有充分的理由推广和改进 Cosmographia 的潜力，因为他是一名仪器制造者，而 Cosmographia 是一部 阿皮亚努斯 描述并图解了从 海马·弗里修斯 的工作室可获得的广泛数学仪器的著作。这本书图解并描述了木制、黄铜和象牙仪器，但文本中甚至还包括了可操作的纸质仪器，称为 volvelles，让读者可以实验所描述的想法。有了提供的 volvelles，读者可以解决日历问题并找到太阳、月亮和行星的位置。

1524年至1540年间的另一部出版物是 阿皮亚努斯 对数学本身而非其应用的最重要贡献。这是他的书 Instrumentum sinuum sive primi，出版于1534年，包含第一张按每弧分计算的 sine 表。像 阿皮亚努斯 的所有其他著作一样，这本书包含了大量数学应用，sine 表被应用于天文学、航海和建筑问题。1534年，阿皮亚努斯 出版了第一张欧洲大地图，但遗憾的是这部作品已不复存在。

1540年后，阿皮亚努斯 变得著名和富有。查理五世授予他更多特权，例如使非婚生子女合法化的权力，以及授予高等学位的权力。

阿皮亚努斯 有一个儿子 Phillip，生于1531年，跟随父亲学习数学。在 阿皮亚努斯 于1552年去世后，Philip 被任命填补因戈尔施塔特大学数学教授的空缺职位。

Kish在[1]中总结了阿皮亚努斯的贡献：-

阿皮亚努斯是天文学和地理学仪器方面的先驱，也是十六世纪这些学科最成功的普及者之一。

Petrus Apianus, also known as Peter Apian, Peter Bennewitz, and Peter Bienewitz, was one of four sons of Martin and Gertrud Bienewitz. He entered the University of Leipzig where he studied mathematics, astronomy and cosmography.

Perhaps we should indicate what the study of cosmography entailed. It was a broad science which set out to provide a mathematical basis for the position of everything in the universe. As such it required someone who specialised in the topic to be an expert in astronomy, geography, mapmaking, navigation, surveying, architecture, mathematical instruments, and sundials. In many ways these can be thought of as the applied mathematical disciplines of Apian's day, and we can certainly consider Apian as a leading applied mathematician. Apian excelled at mathematics and its 16th century applications, and after his studies at Leipzig he moved to Vienna where he continued to study the same broad collection of applied mathematical topics.

It is also worth noting that the early 16th century was an exciting time to be mapping the world. Vasco da Gama had sailed from Portugal round Africa to India in 1498. Christopher Columbus had landed in the Americas in 1492 and in 1522 Ferdinand Magellan had returned to Spain after a round the world voyage. This was close to the time when Apian began to publish. His first work was a world map Typus orbis universalis which he based on earlier 1520 work by Martin Waldsemüller. Apian's second work followed the year after and this was the Isagoge Ⓣ, a geographical commentary on the Typus orbis universalis.

In 1524 Apain published his first work of major importance. This was Cosmographia seu descriptio totius orbis and was a work based largely on Ptolemy. Cosmographia provided an introduction to astronomy, geography, cartography, surveying, navigation, weather and climate, the shape of the earth, map projections, and mathematical instruments. The lavishly illustrated book was far more than an atlas but it did provide sketches of the continents and some of the earliest maps of America.

The 1524 publication of Cosmographia was a modest success but not really a best seller. However, taken with his earlier works, it showed Apian's great talents and these publications were the main reason that he was appointed Professor of Mathematics at the University of Ingolstadt in 1527. From this point his career really took off although the arithmetic book which he published in that year was not a major factor. One aspect of this little work on arithmetic which, like all of Apian's contributions, is highly practical in its aims, was that the title page contained Pascal's triangle. This was the first time that this famous piece of mathematics appeared in print in Europe.

At this time Charles V, the Holy Roman emperor, ruled over large parts of Europe as King of Spain and Archduke of Austria with a Spanish and Habsburg empire covering Europe from Spain and the Netherlands to Austria and Italy. It seems likely that Charles himself had studied cosmography, a useful subject for a ruler of so large an empire, under Apian around 1530. The evidence for this, however, is not conclusive. We know for certain that by the early 1530s Apian had special privileges granted by Charles and in 1540 Apian dedicated his next major work Astronomicon Caesareum to Charles.

Astronomicon Caesareum was an even more lavish work than Cosmographia. It presented much of the same material but in a considerably more elegant and polished way. It contains some important new scientific ideas; for example Apian advocates the use of solar eclipses to determine longitude. The book also contains descriptions of five comets, in particular Halley's comet, and in Astronomicon Caesareum Apian is the first to make the important observation that a comet's tail always points away from the Sun. Astronomicon Caesareum delighted Charles V who, on the strength of the work, appointed Apian court mathematician and he knighted Apian and his three brothers.

Between the publication of Cosmographia in 1524 and Astronomicon Caesareum in 1540, there had been further important publishing events. One was in 1533 when Gemma Frisius published a new edition of Cosmographia. Frisius had spent considerable effort on editing and enlarging Apian's book and it really paid off since this second edition became very much more popular than the first and was a best seller throughout Europe, being translated into all major European languages. Of course Frisius had ample reason to promote and improve the potential of the Cosmographia for he was a maker of instruments and Cosmographia was a work in which Apian had described and illustrated a wide range of mathematical instruments which were available from Frisius's workshop. The book illustrated and described wooden, brass and ivory instruments but there were even working paper instruments included in the text, called volvelles, which let readers experiment with the ideas described. With the volvelles that were supplied readers could solve calendar problems and find the positions of the sun, moon and the planets.

Another publication between 1524 and 1540 was Apian's most important contribution to mathematics itself, rather than its applications. This was his book Instrumentum sinuum sive primi published in 1534 which contained the first sine tables calculated for every minute of arc. Like all other works by Apian this book contained a host of applications of mathematics, and the sine tables are applied to problems of astronomy, navigation and architecture. In 1534 Apian published the first large scale map of Europe but sadly this work is no longer extant.

Following 1540 Apian became famous and wealthy. Charles V granted him more privileges such as the power to make illegitimate children legally legitimate, and also the power to grant higher degrees.

Apian had a son, Phillip, who was born in 1531 and followed his father by studying mathematics. After Apian's death in 1552, Philip was appointed to fill the vacant post of Professor of Mathematics at the University of Ingolstadt.

Kish, in [1], sums up Apian's contribution:-

Apian was a pioneer in astronomical and geographical instrumentation, and one of the most successful popularisers of these subjects during the sixteenth century.