Mifcellanea Cnriofa. j i i 



Shot : For which Reafons the French Engineers 

 in their late Sieges have ufed Mortar-pieces in- 

 clined conftantly to the Elevation of 45-, propor- 

 tioning their Charge of Pouder according to the 

 diftance of the Objetl they intend to ftrike on 

 the Horizon. 



And this is all that need to be faid con- 

 cerning this Problem of (hooting upon Heights 

 and Defcents. But if a Geometrical Conftru&i- 

 on thereof be required ; I think I have one 

 that is as eafy as can be expedted, which I de* 

 duce from the foregoing Analytical Solution* 



1 r ~yy — " 9 and 'tis this* 



having made the right Angle GDF, (Tab. $* 

 Fig* 3 ) make DF= \ />, or greateft Range, 

 and G D == b the Horizontal Diftance, and D B 

 z=:h the perpendicular heighth of the Object ; to 

 be laid upwards from D, if the Objecl; be above 

 the Horizon, or downwards if below it. Paral- 

 lel to G D draw F A, and make it equal to 

 G B the Hypothenufal Diftance of the Object ; 

 and with the Center A and Radius F B = % p 

 Hr h, fweep an Arch, which (hall if the thing be 

 poilible, inter feci: the indeterminate Perpendicular 

 D F in two Points K and L, to which draw *he 

 Lines, GL, GK; I fay, the Angles DGK, 

 DGL, are the Elevations requisite to ftrike the 

 Obje£ B. 



Demonftration, The Square of FK or FL, is 

 equal to F B 9 — GB j: orkf ± h I 2 — bb — hh 

 bt Xfp a ¥ph-~~ bb y and therefore ^ipp^tph — bb 

 » FK=FU and by Confequence DK, 

 Y DL 



