A treatise on the analytical geometry of the point, line, by John Casey

By John Casey

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A treatise on the analytical geometry of the point, line, circle, and conic sections, containing an account of its most recent extensions, with numerous examples

Leopold is extremely joyful to put up this vintage booklet as a part of our huge vintage Library assortment. the various books in our assortment were out of print for many years, and for this reason haven't been obtainable to most people. the purpose of our publishing application is to facilitate swift entry to this gigantic reservoir of literature, and our view is this is an important literary paintings, which merits to be introduced again into print after many a long time.

Additional info for A treatise on the analytical geometry of the point, line, circle, and conic sections, containing an account of its most recent extensions, with numerous examples

Example text

The papyrus problems were generally written with hieratic number symbols, which don’t at all resemble the hieroglyphic symbols. Many students think the hieroglyphic symbols are cute or quaint. The hieratic ­symbols tend to look like messy ink blots. The Rhind papyrus is about 17‐feet long and has arithmetic, algebra, and geometry problems. We even know the name of the scribe who copied it (Ahmes) and approximately when he copied it (1650 bc); but since it is a copy, we have to infer that the mathematics was well known somewhat before that date.

There was a second multiplication technique, where one factor was doubled ­successively and the other factor was cut in half successively. That would generate a table as follows: 12 6 3 1 35 70 140 280 Students always wonder about cutting odd numbers in half. 5, not 1, but the table only shows whole numbers. Well, the Egyptians threw the fractional part away when they used this technique. The next step is to add the numbers in the second column that are opposite odd numbers in the first column.

Ten hundreds have been replaced by one thousand. 5 Ten stones in the tens column have been replaced by a single stone in the ­hundreds column. 6 Twenty stones in the ones column have been replaced by two stones in the tens column. 42 ANCIENT CHINESE MATHEMATICS This manipulation would tell our scribe that 536, 178, and 429 add up to 1143. Notice that we started the addition work in the hundreds column (carrying to the thousands), and worked our way eventually to the ones column. That is the Chinese way.

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