SIR
:
THe
summe
of
what
I
have
heretofore
written
or
spoken
to
you
,
concerning
the
advancement
of
the
Mathematickes
,
is
this
:
As
long
as
men
want
will
,
wit
,
meanes
or
leisure
to
atter●●
those
studies
,
it
is
no
marvaile
if
they
make
no
great
progresse
in
them
.
To
remedy
which
,
I
conceive
these
meanes
not
to
be
amisse
.
1.
To
write
a
Consiliarius
Mathematicus
,
(
so
I
call
it
)
answering
to
these
3.
questions
:
-
Q.
1.
What
fruit
or
profit
ariseth
from
the
study
of
Mathematics
?
-
Q.
2.
What
helpes
are
there
for
the
attaining
this
profitable
knowledge
?
-
Q.
3.
What
order
is
to
be
observed
in
using
these
helpes
?
To
this
purpose
it
should
containe
-
1.
A
plaine
and
popular
discourse
of
the
extent
of
the
Mathematics
,
with
the
profit
that
redounds
,
first
to
the
Student
himselfe
,
and
then
to
the
Country
wherein
there
are
many
such
grounded
Artists
.
-
2.
A
Catalog
of
Mathematicians
and
their
workes
in
this
order
:
-
1.
A
Synopsis
of
all
the
severall
kindes
of
Mathematicall
writings
,
either
extant
in
print
,
or
accessible
Manuscripts
in
public
Libraries
,
with
severall
numbers
set
to
every
kinde
.
-
2.
A
Chronicall
Catalog
of
all
Mathematicians
names
that
ever
were
of
note
,
according
to
the
order
of
the
yeares
when
they
lived
,
with
the
yeare
when
any
of
their
workes
were
first
printed
.
-
3.
A
Catalog
of
the
writings
themselves
,
in
the
order
of
yeares
in
which
they
were
printed
in
any
language
:
And
this
I
would
contrive
thus
:
First
,
the
yeere
of
our
Lord
,
and
then
the
names
of
all
the
Mathematicall
bookes
printed
that
yeare
in
any
country
or
language
,
after
the
usuall
manner
of
Catalogs
;
but
-
1.
adding
the
volume
,
that
is
,
not
onely
what
fold
[
4o
.
8o
.
&c.
]
but
also
the
number
of
leaves
,
that
we
may
estimate
the
bulke
of
the
booke
.
-
2.
praefixing
before
the
title
,
the
yeare
to
which
you
must
looke
backe
to
know
either
when
it
was
written
,
or
when
it
was
last
before
printed
,
in
that
or
any
other
language
.
-
3.
setting
in
the
margent
,
after
the
title
,
-
1.
the
yeare
wherein
it
was
the
next
time
printed
:
-
2.
the
number
of
reference
to
the
Synopsis
in
the
first
page
;
By
which
numbers
one
may
presently
runne
over
all
the
bookes
of
one
sort
,
of
this
or
that
particular
subject
.
-
3.
A
Counsell
directing
a
student
to
the
best
bookes
in
every
kinde
;
In
what
order
,
and
how
to
reade
them
,
What
to
observe
,
what
to
beware
of
in
some
Mathematicasters
,
how
to
proceed
and
keepe
all
.
-
4.
A
Paraenesis
,
First
,
To
all
those
who
have
meanes
and
leisure
,
and
a
wit
not
unapt
for
these
studies
,
to
set
upon
them
in
regard
1.
of
their
profitablenesse
to
the
student
,
and
to
mankinde
,
and
2.
of
that
more
refined
pleasure
of
hunting
out
hidden
truths
,
wrastling
with
difficult
Problemes
,
and
getting
the
victory
;
and
so
much
the
rather
,
because
3.
of
the
great
facility
that
is
now
in
that
study
,
by
reason
of
the
many
helpes
to
spare
much
labour
,
time
and
cost
,
which
our
forefathers
were
forced
to
spend
.
Secondly
,
To
all
those
who
have
understanding
to
estimate
the
worth
of
these
studies
,
and
wealth
wherewith
to
purchase
to
themselves
lasting
honour
by
the
wise
dispensing
of
it
,
to
take
more
notice
of
this
sort
of
students
,
and
to
encourage
them
,
setting
apart
the
choicest
of
them
,
to
perfect
the
inventions
,
to
which
their
Genius
leads
them
:
Especially
,
To
all
Princes
and
Estates
,
whom
it
concernes
to
take
a
course
1.
that
their
dominions
may
be
better
furnished
with
this
sort
of
students
,
2.
that
the
way
may
be
made
lesse
laborious
and
costly
,
3.
that
Mathematica
ingenia
may
be
discovered
and
assisted
.
To
which
end
it
would
be
good
2.
To
erect
a
Public
Library
,
containing
all
those
bookes
,
and
one
instrument
of
every
sort
that
hath
beene
invented
,
with
efficient
revenue
,
1.
to
buy
one
copy
of
all
those
that
shall
be
printed
yearly
in
other
countries
.
and
2.
to
maintaine
a
Library
keeper
of
great
judgement
,
to
whom
it
may
belong
†
-
1.
to
peruse
all
books
of
such
subjects
,
to
be
printed
within
that
country
,
and
1.
suppresse
whatsoever
is
not
according
to
Art
,
that
Learners
be
not
abused
,
and
2.
admonish
the
writers
,
if
they
bring
nothing
but
stale
stuffe
.
-
2.
〈…〉
credit
to
approve
excellent
inventions
,
and
unpartially
to
commend
the
inventors
to
the
rewarders
.
-
3.
to
●eceive
,
record
and
place
one
printed
copy
of
every
booke
so
perused
,
sent
into
the
Library
,
well
bound
at
the
Authors
or
Book-sellers
charge
.
-
4.
to
resolve
any
student
that
enquires
about
any
Probleme
▪
●hether
it
have
beene
done
already
or
no
,
fearing
lest
hee
should
actum
agere
,
and
therefore
perhaps
suppressing
●o●●
〈◇〉
ention
which
he
hath
light
upon
,
but
doubts
it
is
old
and
to
be
found
in
some
of
the
bookes
of
that
Library
.
-
5.
to
receive
,
&c.
all
such
Manuscripts
as
shall
be
brought
thit●er
by
way
of
gift
,
Legacy
,
or
the
like
.
-
6.
to
maintaine
correspondence
with
such
as
himselfe
in
other
countries
,
to
know
what
is
printed
there
.
-
7.
to
take
notice
of
all
his
countrimen
that
are
fit
to
be
teachers
,
&c.
-
8.
to
keepe
a
Catalog
of
all
such
workmen
as
are
able
and
fit
to
be
imployed
in
making
Mathematicall
instruments
and
representations
,
working
upon
wood
,
magnets
,
metalls
,
glasse
,
&c.
-
9.
to
give
testimoniall
,
after
examination
,
to
all
sorts
of
practisers
,
as
Pilots
,
Masters
,
Landmeters
,
Accomptants
,
&c.
of
their
s●●culative
ability
and
practicall
dexterity
,
that
those
that
have
occasion
to
use
such
men
,
be
not
abused
by
unable
undertakers
,
to
their
exceeding
great
damage
.
-
By
the
Catalog
,
men
might
be
informed
,
in
that
multitude
of
bookes
,
with
which
the
world
is
now
pestered
,
what
the
names
are
of
those
bookes
that
tend
to
this
study
onely
.
-
In
the
Library
,
they
might
finde
the
bookes
themselves
,
reade
them
,
and
if
they
liked
them
,
know
whither
to
send
to
buy
them
,
Besides
,
any
,
whether
forreiners
on
others
,
might
have
recourse
thither
,
and
learne
what
helps
that
country
would
afford
them
in
these
studies
.
-
And
this
is
the
best
course
that
I
can
thinke
on
for
the
making
use
of
such
helpes
as
we
have
already
.
If
men
desire
better
helpes
,
let
them
employ
fit
Artists
3.
To
write
and
publish
these
three
new
Treatises
:
†
-
1.
Pandectae
Mathematicae
,
Comprehending
as
cleerly
,
orderly
,
thriftily
,
and
ingenuously
as
may
be
,
whatsoever
may
be
gathered
out
of
all
those
Mathematicall
bookes
and
inventions
that
were
before
us
,
or
that
may
be
inferred
as
Consectaries
thereon
;
citing
,
at
the
end
of
every
period
or
proposition
,
the
ancientest
Author
in
which
it
is
found
,
and
branding
all
later
writers
if
they
be
taken
stealing
,
or
borrowing
without
acknowled●●●ent
,
or
[
which
is
worse
]
expresly
arrogating
to
themselves
any
other
mans
inventions
.
This
would
bring
that
〈◇〉
Library
into
farre
lesse
roome
,
to
the
saving
of
more
labour
,
time
and
cost
,
to
all
after-students
,
than
men
can
yet
well
Imagine
.
But
because
this
also
would
be
too
great
and
cumber
some
to
carry
about
us
,
Let
there
be
composed
-
2.
Comes
Mathematicus
,
Comprehending
in
a
pocket-booke
,
[
and
therefore
as
briefly
as
may
be
]
the
usefullest
Tables
and
the
Precepts
for
their
use
,
in
solving
all
Problemes
,
whether
purely-Mathematicall
,
or
applied
to
such
practices
as
mens
various
occasions
may
require
.
-
And
lastly
,
that
in
this
kinde
of
Learning
also
,
we
be
no
longer
tyed
to
bookes
,
Let
there
be
composed
-
3.
Mathematicus
{αβγδ}
,
or
An
instruction
,
shewing
how
any
Mathematician
that
will
take
the
paines
,
may
prepare
himselfe
,
so
,
as
that
he
may
,
though
he
be
utterly
destitute
of
bookes
or
instruments
,
resolve
any
Marhematicall
Probleme
as
exactly
as
if
he
had
a
complete
Library
by
him
.
And
this
is
the
Idéa
,
which
I
have
long
framed
to
my selfe
,
according
to
my
fashion
,
with
whom
this
〈…〉
●●ted
truth
,
that
the
surest
way
to
come
to
all
possible
excellency
in
any
thing
,
is
to
propose
to
our selves
the
〈…〉
we
can
imagine
,
then
to
seeke
the
meanes
tending
thereto
,
as
rationally
as
may
be
,
and
to
prosecute
it
with
〈…〉
gence
;
yet
,
if
the
Idéa
prove
too
high
for
us
,
to
rest
our selves
content
with
approximation
.
As
for
this
present
Idéa
,
I
am
so
farre
from
counting
it
meerely-impossible
,
that
I
see
not
why
it
might
not
be
performe●…
one
man
,
without
any
assistants
,
provided
that
he
were
neither
distracted
with
cares
for
his
maintenance
,
nor
diverted
by
o●…
employments
.
The
excellency
of
this
worke
,
makes
me
wish
mine
owne
nation
the
honour
of
first
undertaking
and
perfecting
this
desig●…
And
I
conceive
I
have
some
reason
to
hope
that
it
will
be
so
.
For
,
though
I
know
few
or
none
that
are
both
able
and
willing
promote
designes
of
this
nature
,
yet
can
I
not
therefore
be
persuaded
that
this
Kingdome
is
so
destitute
of
learned
Nob●…
and
Gentry
,
that
there
can
be
found
none
to
countenance
and
advance
this
part
of
Learning
,
even
in
this
way
,
if
they
co●…
see
it
possible
and
likely
to
be
effected
.
As
for
the
Library
and
Catalog
,
there
can
be
no
doubt
but
they
may
easily
be
had
,
if
mony
be
not
wanting
.
Nor
is
it
unlik●…
that
divers
of
this
nation
(
if
they
be
set
apart
for
it
)
are
able
to
compose
the
other
3.
new
Treatises
;
For
though
I
know
●…
such
,
yet
I
persuade
my selfe
there
may
be
found
amongst
us
men
able
to
encounter
all
the
difficulties
,
and
to
endure
all
the
●…
bour
,
that
they
must
needs
meet
with
in
the
raising
of
so
great
a
Fabricke
.
And
I
the
rather
beleeve
that
there
are
many
su●…
because
for
mine
owne
part
,
notwithstanding
the
want
of
Counsell
and
helpes
in
that
study
,
and
the
innumerable
diversions
a●…
distractions
that
I
have
had
,
I
am
neverthelesse
come
to
such
a
confidence
of
my
understanding
the
depth
of
that
study
,
tha●…
were
I
to
pen
those
Pandects
,
I
should
lay
heavier
lawes
upon
my selfe
,
than
I
have
already
mentioned
;
namely
,
First
to
l●…
downe
such
an
exact
Method
or
description
of
the
processe
of
Mans
reason
in
inventions
,
that
afterward
it
should
be
imput●…
meerly
to
my
negligence
and
disobedience
to
my
owne
lawes
,
[
and
not
to
their
insufficiency
]
if
,
from
my
first
grounds
,
see●…
or
principles
,
I
did
not
,
in
an
orderly
way
,
according
to
that
praescribed
Method
,
deduce
,
not
onely
all
that
ever
is
to
be
fou●…
in
our
Antecessors
writings
,
and
whatsoever
they
may
seeme
to
have
thought
on
,
but
also
all
the
Mathematicall
invention
Theoremes
,
Problemes
and
Precepts
,
that
it
is
possible
for
the
working
wits
of
our
successors
to
light
upon
,
and
that
in
one
ce●…
taine
,
unchanged
order
,
from
the
first
seeds
of
Mathematics
,
to
their
highest
and
noblest
applications
,
as
well
as
to
the
mean●…
and
most
ordinary
.
Not
setting
them
down
at
randon
as
they
come
in
my
head
,
as
those
before
us
have
done
,
so
that
they
seeme
●…
have
light
upon
their
Problemes
and
the
solutions
of
them
by
chance
,
not
to
have
found
them
by
one
perpetuall
,
constant
,
in●…
riable
processe
of
Art.
Yet
such
an
Art
may
men
invent
,
if
they
accustome
themselves
,
as
I
have
long
done
,
to
consider
,
not
one●…
the
usefulnesse
of
mens
workes
,
and
the
meaning
and
truth
of
their
writings
,
but
also
how
it
came
to
passe
that
they
fell
upon
su●…
thoughts
,
and
that
they
proposed
to
themselves
such
ends
,
or
found
out
such
meanes
for
them
.
Were
these
Pandects
thus
made
and
finished
,
I
suppose
it
is
manifest
,
that
by
their
orderly
,
rationall
and
uniforme
co●…
pleatnesse
,
above
all
that
hath
beene
hitherto
written
,
they
would
spare
after-students
much
labour
and
time
that
is
now
spe●…
in
seeking
out
of
bookes
,
and
disorderly
reading
them
,
and
struggling
with
their
cloudy
expressions
,
unapt
representations
,
d●…
ferent
Methods
,
confusions
,
tautologies
,
impertinencies
,
falshoods
by
paralogismes
and
pseudographemes
,
uncertainties
b●…
cause
of
insufficient
demonstrations
,
&c.
besides
much
cost
also
,
now
throwne
away
upon
the
multitude
of
bookes
,
the
gre●…
ter
part
whereof
they
had
perhaps
beene
better
never
to
have
seene
.
And
it
may
be
some
would
like
the
Method
of
that
worke
so
well
,
as
to
extend
it
farther
,
and
apply
it
to
other
studies
;
●…
speculation
imitating
this
my
warinesse
,
that
no
falshood
be
admitted
,
and
no
truth
omitted
;
and
for
practice
enuring
themselve●…
Any
subject
being
propounded
,
to
determine
the
number
of
all
the
Problemes
that
can
be
conceived
concerning
it
,
and
A●…
Probleme
being
propounded
,
demonstratively
to
shew
either
all
the
meanes
of
its
solution
,
or
the
impossibility
of
it
:
and
if
●…
then
whether
it
be
not
yet
,
or
not
at
all
possible
.
Men
would
easily
see
how
to
contract
these
Pandects
into
a
pocket-booke
for
their
ordinary
use
.
But
so
to
lay
them
up
in
th●…
heads
,
as
to
need
no
booke
at
all
[
according
to
that
desideratum
of
mine
,
to
have
a
Mathematicus
{αβγδ}
]
will
perhaps
see●…
utterly
impossible
to
most
:
No
man
,
that
ever
I
heard
of
,
having
proposed
such
a
scope
to
himselfe
before
.
But
perha●…
they
will
conceive
it
more
possible
,
if
it
please
them
to
suspend
their
judgements
,
till
they
have
considered
what
meanes
●…
be
used
to
fortifie
the
imagination
,
to
prompt
the
memory
,
to
regulate
our
reason
,
and
what
effects
may
be
produced
by
●…
uniting
of
these
meanes
,
and
the
constant
exercising
of
them
.
For
mine
owne
part
,
the
consideration
of
the
incomparable
excellency
,
unstained
pleasure
,
unvaluable
profitablenesse
,
and
●…
doubted
possibility
of
this
whole
designe
,
hath
prevailed
so
farre
with
me
,
that
notwithstanding
all
the
discouragements
tha●…
have
met
withall
,
I
have
done
more
towards
it
than
bare
Idéa
,
.