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6.2 
Mathematical Concepts 
6.2.1 Fundamentals and Precursors 
Development oi mathematics as a discipline of logic did not exist 
before about 1000 B.C. The Greek philosopher Aristotle (350 B.C.)- re- 
feired to the process of optical projection of images. Leonardo da Vinci 
explored the disciplines of optics, geometry and mechanics. In 1492 he 
demonstrated the principles of optical perspectivity (MacLeish 1977), 
which provides the foundation of photogrammetry even today. Albrecht 
Ddrei (1471-1528) in 1525 constructed samples of mechanical devices to 
make true perspective drawings of nature and studio scenes as well as for 
producing stereoscopic drawings (ASPRS 1980). The German astronomer 
Johannes Kepier in 1600 gave a precise definition of stereoscopy. Aughtread 
of England in 1574 developed the first slide rule and soon thereafter John 
Napier (1550-1617) published tables of logarithms and Blaise Pascal (1623- 
1662) established the concept of metrology and gave the world a desk calcu 
lator. Isaac Newton (1642-1727) and Gottfried von Leibnitz (1646-1716) 
firmly established the concepts of differential and integral calculus♦ 
Concepts of inverse central perspective and space resection of conjugate 
images were first discussed by J. Henry Lambert (1728-1777) in his book 
"Freie Perspective" in 1759. 
Wheatstone of England presented in 1838 the stereoscope. one most 
important tool used in photogrammetry. The practice of photogrammetry 
could be started only after Arago and Niepce announced a "Heliographic 
Process", based on which Louis J.M. Daguerre (1789-1851) presented to the 
French Academy of Arts and Sciences in 1837 the photographs which he called 
"daguerrotypes". The coining of the term "photogrammetry" in 1855 by 
Kersten with its introduction by Mevdenbauer in 1867 to international 
literature, the first German textbook on photogrammetry by Koppe (1889) 
and Aimé Laussedat's classic work on French photogrammetry (1898) are some 
of the milestones of analytical photogrammetry recorded in history (ASPRS 
1980). 
Hauck (1883) established the relationship between projective geo 
metry and photogrammetry. 
Ernst Abbe, the cofounder of the German Zeiss Works in 1871 started 
intense studies and tests for optical elements on the basis of rigorous 
mathematical analyses. F. Stolze discovered the principle of the floating 
mark in 1892 while Carl Pulfrich also of the Zeiss group developed a prac 
ticable method of measuring and deriving spatial dimensions from stereo 
photographic images with floating marks. He presented in 1901 the Zeiss- 
Pulfrich Stereocomparator by supplementing Eduard von Orel's (1877-1941) 
first prototype Stereoautograph at the 73 rd Conference of Natural Scien 
tists and Physicians held at Hamburg. Separately, a similar stereocom 
parator was invented in 1901 by Henry G. Fourcade (1865-1948) of South 
Africa. He presented this at the Philosophical Society of Cape Town. 
Sebastian Finsterwalder (1862-1951) in a series of publications 
during 1899 to 1937 established a very strong foundation for analytical 
photogrammetry. In these he brought about the geometric relations which 
govern resection and intersection as well as re1ative and absolute orien 
tations. He predicted the future possibility of nadir point triangulation