t n i 
T R I 
T R I 
inent, or bring it in ignoramus and if the 
bill is found, the prisoner is brought to the 
bar of the court, and the clerk of the ai - - 
raigns calling him by his name, desires 
him to hold up his hand, saying, “ Thou 
art indicted by the name of , for such 
a felony, & c. (setting forth the crime laid 
[in the indictment). How sayest thou ; art 
thou guilty of this felony whereof thou 
art indicted, or not guilty r” To which 
the prisoner answering, “ Not guilty,” the 
clerk says, “ Culprit, how wilt thou be tried?” 
[whereupon the defendant answers, “ By God 
and my country;” which plea of the prisoner 
the clerk records, and then the panel of the 
petty-jury is called over. 
After the jury are sworn, and the indict- 
ment is read over to them, and they are 
(’charged, the evidences on both sides, for and 
against the prisoner, are called, sworn, and 
examined in open court; after which the jury 
bring in their verdict ; and if they find the pri- 
soner guilty, their verdict is recorded, and 
the prisoner is taken from the bar : but if 
they bring him in not guilty, the prisoner is 
| discharged. On the prisoner being brought 
in guilty, proclamation is made for all per- 
sons to keep silence, upon which the prisoner 
is again brought to the bar, and the verdict re- 
peated: after which sentence is passed on 
him, and an order or warrant is made for 
his execution. 
The methods of trial, in our civil courts, 
are as follows : via. The declaration is first 
drawn for the plaintiff, and when the appear- 
anceof the defendant is entered, it has been 
usual to deliver it with an imparlance to the 
defendant’s attorney ; and the term following, 
rule is to be given with the secondary for the 
defendant to plead by such a day, or else the 
plaintiff is to have judgment : and the defend- 
ant having pleaded, a copy of the issue is 
made by the plaintiff, and delivered to the 
defendant’s attorney, at the same time giving 
him notice of the trial ; in order to which the 
I venire facias must be taken out and returned 
by the sheriff: and likewise the habeas cor- 
pora, or distringas, to bring in the jury; on 
which the record is made up, and the parties 
proceed to trial by their counsel and witnesses; 
and the jury give in their verdict, &c. But 
in case the defendant neglects to plead, and 
suffers it to go by default, on entering such 
a judgment, a writ of inquiry of damages is 
awarded returnable next term, notice of the 
i execution whereof the defendant’s attorney is 
| to have ; and which being executed, and the 
damages inserted in a schedule annexed to 
the writ, a rule is given, and costs are taxed 
by the prothonotary, & c. 
TRIANDRIA, in the Linnsean system of 
botany, a class of plants, the third in order; 
comprehending all such plants as have her- 
maphrodite flowers, with three stamina, or 
male parts, in each ; whence the name. See 
Botany. 
TRIANGLE, in geometry, a figure 
bounded or contained by three lines or sides, 
\ and which consequently has three angles, 
from whence the figure takes its name. 
Triangles are either plane, or spherical, or 
curvilinear. Plane when the three sides of 
the triangle are right lines ; but spherical 
when some or all of them are arcs of great 
circles on tlie sphere. 
Plane triangles take several denominations, 
VOL. II. 
both from the relation of their angles, and of 
their sides, as below. See Geometry. 
The chief properties of plane triangles arc 
as follow, viz. In any plane triangle, 
1. The greatest side is opposite to the 
greatest angle, and the least side to the 
least angle, &c. Also, if two sides are 
equal, their opposite angles are equal ; and if 
the triangle is equilateral, or has all its sides 
equal, it will also be equiangular, or have all 
its angles equal to one another. 2. Any side 
of a triangle is less than the sum, but greater 
than the difference, of the other two sides. 
3. The sum of all the three angles, taken to- 
gether, is equal to two right angles. 4. 'If 
one side of a triangle is produced out, the 
external angle, made by it and the adjacent 
side, is equal to the sum of the two opposite 
internal angles. 5. A line drawn parallel to 
one side of a triangle, cuts the other two sides 
proportionally, the corresponding segments 
being proportional, each to each, and to the 
whole sides ; and the triangle cut off is similar 
to the whole triangle. 
If a perpendicular is let fall from any an- 
gle of a triangle, as a vertical angle, upon the 
opposite side as a base ; then, 6. The rectan- 
gle of the sum and difference of the sides, is 
equal to twice the rectangle of the base and 
the distance of the perpendicular from the 
middle of the base. Or, which is the same 
thing in other words, 7. The difference of 
the squares of the sides, is equal to the dif- 
ference of the squares of the segments of the 
base. Or, as the base is to the sum of the 
sides, so is the difference of the sides to the 
difference of the segments of the base. 8. 
The rectangle of the legs or sides is equal to 
the rectangle of the perpendicular and the 
diameter of the circumscribing circle. 
If a line is drawn bisecting any angle, to 
the base or opposite side ; then, 9. The seg- 
ments of the base, made by the line bisect- 
ing the opposite angle, are proportional to the 
sides adjacent to them. 10. The square of 
the line bisecting the angle, is equal to the dif 1 
ference between the rectangle of the sides and 
the rectangle of the segments of the base. 
If a line is drawn from any angle to the 
middle of the opposite side, or bisecting the 
base, then, 11. The sum of the squares of the 
sides, is equal to twice the sum of the squares 
of half the base and the line bisecting the 
base. 12. The angle made by the perpendi- 
cular from any angle and the line drawn from 
the same angle to the middle of the base, is 
equal to half the difference of the angles at 
the base. 13. If through any point within a 
triangle three lines are drawn parallel to the 
three sides of the triangle, the continual pro- 
ducts or solids made by the alternate seg- 
ments of these lines will be equal. 14. If 
three lines are drawn from the three angles 
through any point within a triangle, to the 
opposite sides; the solid products of the al- 
ternate segments of the sides are equal, viz. 
15. Three lines drawn from the three angles of 
a triangle to bisect the opposite sides, or to the 
middle of the opposite sides, do all intersect 
one another in the same point, and that point 
is the centre of gravity of the triangle ; and the 
distance of that point from any angle is equal 
to double the distance from the opposite side, 
or one segment of any of these lines is double 
the other segment : moreover the sum of the 
squares of the three bisecting lines is | of the 
8)7 
sum of the squares of the three sides of the 
triangle. 16. Three perpendiculars bisecting 
the three sides of a triangle, ail intersect in one 
point, and tiiat point is the centre of the cir- 
cumscribing circle. 17. Three lines bisect- 
ing the three angles of a triangle, all intersect 
in one point, and that point is the centre of 
the inscribed circle. 18. Three perpendicu- 
lars drawn from the three angles ot a trian- 
gle upon the opposite sides, all intersect in 
one point. 19. Any triangle may have a cir- 
cle circumscribed about it, or touching all its 
angles, and a circle inscribed within it, or 
touching all its sides. 20. The square of the 
side of an equilateral triangle is equal to three 
times the square of the radius of its circum- 
scribing circle. 21. If the three angles of 
one triangle are equal to the three angles of 
another triangle, each to each, then those two 
triangles are similar, and their like sides are 
proportional to one another, and the areas of 
the two triangles are to each other as the 
squares of their like sides. 22. If two tri. 
angles have any three parts of the one (ex- 
cept the three angles) equal to three corn s- 
ponding parts ot the other, each to each, 
those two triangles are not only similar, but 
also identical, or having all their six corres- 
ponding parts equal, and their areas equal. 
23. Triangles standing upon the same base, 
and betw een the same parallels, are equal ; and 
triangles upon equal bases, and having equal 
altitudes, are equal. 24. Triangles on equal 
bases, are to one another as their altitudes, 
and triangles of equal altitudes are to one 
another as their bases ; also equal triangles 
have their bases and altitudes reciprocally 
proportional. 25. Any triangle is equal to 
halt its circumscribing parallelogram ; or half 
the parallelogram on the same or an equal 
base, and of the same or equal altitude. 
26. Therefore the area of any triangle is 
found by multiplying the base by the alti- 
tude, and taking half the product. 27. The 
area is also found thus : Multiply any two 
sides together, and multiply the product by 
the sine of their included angle, to radius 1 
and divided by 2. 28. The area is also other- 
wise found thus, when the three sides are 
given: Add the three sides together, and take 
half their sum; then from this half sum sub- 
tract each side severally, and multiply the 
three remainders and the half sum continu- 
ally together; then the square root of the 
last product will be the area of the triangle. 
29. In a right-angled triangle, if a perpendi- 
cular is let fall from the right angle upon the 
hypothenuse, it will divide it into two other 
triangles similar to one another, and to the 
whole triangle. 30. In a right-angled trian- 
gle, the square of the hypothenuse is equal to 
the sum of the squares of tire two sides ; and, 
in general, any figure described upon the hy- 
pothenuse is equal to the sum of two similar 
figures described upon the two sides. 31 
In an isosceles triangle, if a line is drawn from 
the vertex to any point in the base, the 
square of that line, together with the rect- 
angle of the segments of the base, is equal to 
the square of the side. 32. If one angle of a 
triangle is equal to 120°, the square" of the 
base will be equal to the squares of both the 
sides, together with the rectangle of those 
sides ; and if those sides are equal to each 
other, then the square of the base will be equal 
to three times the square of one side, or equal 
to twelve times the square of the perpend ieu- 
