scholarly journals A Synthetic Proof of Pappus’ Theorem in Tarski’s Geometry

2016 ◽  
Vol 58 (2) ◽  
pp. 209-230 ◽  
Author(s):  
Gabriel Braun ◽  
Julien Narboux
Keyword(s):  
Synthetic Proof

scholarly journals Synthetic Proof for the Structures of Maturinone and Cacalol

1977 ◽  
Vol 50 (4) ◽  
pp. 961-966 ◽  
Author(s):  
Yoshinobu Inouye ◽  
Yuji Uchida ◽  
Hiroshi Kakisawa
Keyword(s):  
Synthetic Proof

α-Cubebene and β-cubebene. Synthetic proof of gross structure.

1969 ◽  
Vol 10 (16) ◽  
pp. 1251-1253 ◽  
Author(s):  
Edward Piers ◽  
Ronald W. Britton ◽  
William de Waal
Keyword(s):  
Synthetic Proof

A synthetic proof of de Longchamps' chain

1971 ◽  
Vol 69 (3) ◽  
pp. 393-400 ◽  
Author(s):  
M. S. Longuet-Higgins
Keyword(s):  
Synthetic Proof

A famous chain of theorems, due originally to de Longchamps (l) and afterwards rediscovered by Pesci(2), Morley(3) and Grace(4), goes as follows:(1) Given four lines in a plane, the four circumcentres O3 of the triangles formed by omitting each one of the lines in turn lie all on the same circle C4 with centre O4 say.(2)Given five lines in a plane, the centres O4 of the five circles C4 obtained by omitting each of the five lines in turn lie all on the same circle C6 with centre O5 say.And in general(3) Given (n+1) lines in a plane, the (n+1) centres On of the circles Cn+1 formed by omitting each of the lines in turn lie all on the same circle Cn+1 with centre On+1.

Synthesis ofLycopodiumAlkaloids. I. A Synthetic Proof for the Structure of Lyconnotine

1964 ◽  
Vol 86 (12) ◽  
pp. 2533-2534 ◽  
Author(s):  
Z. Valenta ◽  
P. Deslongchamps ◽  
R. A. Ellison ◽  
K. Wiesner
Keyword(s):  
Synthetic Proof

A Synthetic Derivation of the Class of the Φ Conic

1935 ◽  
Vol 29 ◽  
pp. xxiv-xxv
Author(s):  
H. E. Daniels
Keyword(s):  
Simple Proof ◽  
Analytical Methods ◽  
Familiar Result ◽  
Synthetic Proof

The theorem that a line cutting a pair of conies in four harmonically separated points envelopes a conic, called the Φ conic, is a familiar result which admits of a simple proof by analytical methods. A synthetic proof, however, if we exclude the use of (2, 2) correspondences, is rather elusive. I have not been able to find such a proof in any book, and the only one published as far as I am aware is that set as a question in the 1934 Mathematical Tripos, due to Mr F. P. White. The proof written out below is rather more direct and may therefore be worth recording.

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