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=== Hellenistic medicine === There was not a defined societal structure for healthcare during the age of Hippocrates. At that time, society was not organized and knowledgeable as people still relied on pure religious reasoning to explain illnesses. Hippocrates introduced the first healthcare system based on science and clinical protocols. Hippocrates' theories about physics and medicine helped pave the way in creating an organized medical structure for society. In medicine, Hippocrates (c. 460370 BCE) and his followers were the first to describe many diseases and medical conditions and developed the Hippocratic Oath for physicians, still relevant and in use today. Hippocrates' ideas are expressed in The Hippocratic Corpus. The collection notes descriptions of medical philosophies and how disease and lifestyle choices reflect on the physical body. Hippocrates influenced a Westernized, professional relationship among physician and patient. Hippocrates is also known as "the Father of Medicine". Herophilos (335280 BCE) was the first to base his conclusions on dissection of the human body and to describe the nervous system. Galen (129 c. 200 CE) performed many audacious operations—including brain and eye surgeries— that were not tried again for almost two millennia.

=== Greek mathematics ===

In Hellenistic Egypt, the mathematician Euclid laid down the foundations of mathematical rigor and introduced the concepts of definition, axiom, theorem and proof still in use today in his Elements, considered the most influential textbook ever written. Archimedes, considered one of the greatest mathematicians of all time, is credited with using the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi. He is also known in physics for laying the foundations of hydrostatics, statics, and the explanation of the principle of the lever.

=== Other developments === Theophrastus wrote some of the earliest descriptions of plants and animals, establishing the first taxonomy and looking at minerals in terms of their properties, such as hardness. Pliny the Elder produced one of the largest encyclopedias of the natural world in 77 CE, and was a successor to Theophrastus. For example, he accurately describes the octahedral shape of the diamond and noted that diamond dust is used by engravers to cut and polish other gems owing to its great hardness. His recognition of the importance of crystal shape is a precursor to modern crystallography, while notes on other minerals presages mineralogy. He recognizes other minerals have characteristic crystal shapes, but in one example, confuses the crystal habit with the work of lapidaries. Pliny was the first to show amber was a resin from pine trees, because of trapped insects within them. The development of archaeology has its roots in history and with those who were interested in the past, such as kings and queens who wanted to show past glories of their respective nations. The 5th-century-BCE Greek historian Herodotus was the first scholar to systematically study the past and perhaps the first to examine artifacts.