551276
[Translation: triangular ]
or 2 in 3; 2 in 4; 2 in 5; 2 in 6 ; 2 in 7
or the diagonalls
[Commentary:
At the bottom of the page is a reference to Commandino's Euclidis elementorum XV
(Euclid . However the relevant passage is to be found on page 201v (not 102), as part of a Scholium following Book XI, Proposition 23.
(Euclid 1572, . Commandino's statement is:
Ex planis quotlibet datis angulis, quorum uno reliqui sint maiores quomodocumque sumpti, solidum angulum constituere, oportet autem datos angulos quatuor rectis esse minores.
From any number of given plane angles, given one of which, the rest are greater, however taken, to make a solid angle it is necessary that the given angles are less than four right angles.]
Ex planis quotlibet datis angulis, quorum uno reliqui sint maiores quomodocumque sumpti, solidum angulum constituere, oportet autem datos angulos quatuor rectis esse minores.
From any number of given plane angles, given one of which, the rest are greater, however taken, to make a solid angle it is necessary that the given angles are less than four right angles.]
[Commentary:
Euclid's is:
To construct a solid angle out of three plane angles two of which, taken together in any manner, are greater than the reamining one: thus the three angles must be less than four right angles. ]
To construct a solid angle out of three plane angles two of which, taken together in any manner, are greater than the reamining one: thus the three angles must be less than four right angles. ]
1) De quadrilatero,
et cæteris
[Translation: On quadrilaterals and other ]
et cæteris
[Translation: On quadrilaterals and other ]
[Translation: triangular ]
or 2 in 3; 2 in 4; 2 in 5; 2 in 6 ; 2 in 7
or the diagonalls
solidus angulus ex
quotlibet datis non
potest constitui sine
hoc
[Translation: It is not possible to construct a solid angle from any given number [of plane angles] without this problem.
vide. Euclid. lib. 11
pag. 102.
[Translation: See Euclid Book XI, page 202 of ]
quotlibet datis non
potest constitui sine
hoc
[Translation: It is not possible to construct a solid angle from any given number [of plane angles] without this problem.
vide. Euclid. lib. 11
pag. 102.
[Translation: See Euclid Book XI, page 202 of ]
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