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I. An Account of the Caufe of the late remarkable Appea- 
rance of the Tlanet Venus, feen this Summer , for ma- 
ny Days together , in the Day time. By Edm. Halley, 
% S. Seer, 
I T may juftly be reckoned one of the principal Ufes of the 
Mathematical Sciences, that they are in many Cafes able 
to prevent the Superftition of the unskilful Vulgar; and by 
(liewing the genuine Caufes of rare Appearances, to deliver 
them from the vain apprehenfions they are apt to entertain 
of what they call Prodigies ; which fometimes, by the Artifices 
of defigning Men, have been made ufe of to very evil purpofes. 
Of this kind was the late Appearance of Venus in the Day 
time, generally taken notice of about London and elfewhere ; 
and by fome reckoned to be Prodigious. This put me upon the 
enquiry, how it came to pafs that at that time the Planet 
(liould be io plainly feen by Day, whereas flic rarely (hews 
her felf fo, unlefs to thofe who know exactly where to look for 
her. To refolve this, the following Problem arofe, viz. To 
find the Situation of the Planet in refped of the Earth, when 
the Area of the illuminated part of her Disk is a Maximum. 
To inveftigate this Maximum, l fo'und it requisite to ajjume 
the following Lemmata. I. That the vifible Areas of the Disk 
of the fame Planet , at differing Diflances, are always recipro- 
cally as the Squares of thofe Diftances; which is evident from 
the firft Principles of Of ticks. I!. That the Area of the whole 
Disk of the Planet is to the Area of the illuminated Part there- 
of, as the Diameter of a Circle to the Verfed-Sine of the exte- 
riour Angle at the Planet , in the Triangle at whofe Angles are 
the Sun, Earth, and Planet. 111. That in all plain Triangles, 
four times the Re&angleof the Sides containing any Angle, is 
to the excels of the Square of the Sum of the Sides above the 
Square of the Bafe, as the Diameter is to the Verfed-Sine of 
the 
