{2d04 idea (cognitio) adaequata}

Meaning Adaequatio of ideas (NOT of causes, for causes see {3d01 causa adaequata ^ partiale}. The formal definition mainly specifies what adequacy is NOT: it is NOT the conformity with what the idea is about, because an adequate idea is true with geometrical certainty and such is not to be established by checking correspondence with the object. E.g. when you measure the three angles of a triangle neatly drawn on paper, you might arrive at 180o, within a margin of less half a degree. But that is not why the idea of the angles forming 180o is true. It is true because it is adequate. But  definition {2d04} tells us little about what makes an idea adequate, except that such an idea has proprietates sive denominationes intrinsecas of a true idea. The string "properties of some thing" is equivalent to the string "what a thing has", so adds nothing to the verb "has", itself empty. So we are left with the Latin denominatio. That  surely is not a clear and distinct term. It occurs only one more time where it is simply repeated to refer to the definition. The following dictionary meanings can be found: 1. A leading or drawing off of water from a stream or source. 2. The act of receiving anything from a source; the act of procuring an effect from a cause, means, or condition, as profits from capital, conclusions or opinions from evidence. 3. The act of tracing origin or descent, as in grammar or genealogy; as, the derivation of a word from an Indo-European root. 4. The state or method of being derived; the relation of origin when established or asserted. 5. That from which a thing is derived. 6. That which is derived; a derivative; a deduction. 7. The use of a single characteristic or name of an object to identify an entire object or related object.
The common denominator of this impressive list seems that to establish adequacy, observing the truth of something in practice is insufficient; the truth must somehow be proven. And if you want to know in what sense things are proven in Ethica, you could best simply pass over all proofs and find for yourself the common "denominator".
Summarizing and combining with what turns out later in the exposition of Ethica:
A. The truth (veritas) of an adequate idea is caused by the idea itself (internally)
B. An inadequate idea can (by a stroke of luck during its imagination) be true (vera), but this is caused externally, hence proves nothing.
C. A false idea is (by the meaning of falsity) always false-by-accident, thus falsity is always caused externally, there can never be anything wrong with an inadequate idea in itself.
D. The complete library of adequate ideas is only in God = natura-sense 2 = substance (or in a perfect mind, which actu no human can have).
Mantras [what is] idea adaequata
cognitio adaequata
Related concepts vera , vere concipere, see below, sometimes used for adaequate concipere but strictly not equivalent: imaginatio may lead to true (verae) ideas by a stroke of luck, in which case the true ideas are not adequate.
 {3d01 causa adaequata ^ partiale}
Occurrence [geomap]
NOT linked pleonastic uses ("adaequate sequi")
{1p30 Intellectus comprehendere}                                          ...inadequate ideas are in the mind and in the attribute of thought, but not in the intellect. The others, the adequate ones, are in the intellect, and hence for those holds:  ...
 ...that which is contained in the intellect in representation must necessarily be granted in nature. ... ...id quod in intellectu objective continetur, debet necessario in natura dari. ....
{2d04 idea (cognitia) adaequata}                                               ...adaequata is emphatically explained NOT to be equivalent by definition [mng-eqv] to vera but adaequata it will be proven to imply vera (the inverse does not hold) in {2p34})
...an adequate idea...an idea which, in so far as it is considered in itself, without relation to the object, has all the properties or intrinsic marks of a true idea. ...ideam adaequatam ....ideam quae quatenus in se sine relatione ad objectum consideratur, omnes verae ideae proprietates sive [mng-eqv] denominationes intrinsecas habet.
...I say intrinsic, in order to exclude that mark which is extrinsic, namely, the agreement between the idea and its object (ideatum). ...Dico intrinsecas ut illam secludam quae extrinseca est nempe convenientiam ideae cum suo ideato.
{2p11c mens partem infiniti intellectus Dei}                                    ...the theory of percipere and inadaequate percipere...
... when we say, that the human mind perceives this or that, we make the assertion, that God has this or that idea, not in so far as he is infinite, but in so far as he is displayed through the nature of the human mind, or in so far as he constitutes the essence of the human mind; and when we say that God has this or that idea, not only in so far as he constitutes the essence of the human mind, but also in so far as he, simultaneously with the human mind, has the further idea of another thing, we assert that the human mind perceives a thing in part or inadequately. ...cum dicimus mentem humanam hoc vel illud percipere, nihil aliud dicimus quam quod Deus non quatenus infinitus est sed quatenus per naturam humanae mentis explicatur sive [mng-eqv] quatenus humanae mentis essentiam constituit, hanc vel illam habet ideam et cum dicimus Deum hanc vel  illam ideam habere non tantum quatenus naturam humanae mentis constituit sed quatenus simul cum mente humana alterius rei etiam habet ideam, tum dicimus mentem humanam rem ex partesive sive [mng-eqv] inadaequate percipere.
{2p25 corporis externi cognitionem non involvit}              ...God = natura-sense 2 = substance has both the adequate idea of something and our idea of it, which may be inadequate (confused) due to the limitations of the thing's  impact on us...
...The idea of each modification [Lat: affectiones] of the human body does not involve an adequate knowledge of the external body. ... Idea cujuscunque affectionis corporis humani adaequatam corporis externi cognitionem non involvit.
...We have shown that the idea of a modification [Lat: affectiones] of the human body involves the nature of an external body, in so far as that external body conditions the human body in a given manner. But, in so far as the external body is an individual, which has no reference to the human body, the knowledge or idea thereof is in God ... in so far as God is regarded as affected by the idea of a further thing, which ... is naturally prior to the said external body. Wherefore an adequate knowledge of the external body is not in God, in so far as he has the idea of the modification [Lat: affectiones] of the human body... ... ideam affectionis corporis humani eatenus corporis externi naturam involvere ostendimus ... quatenus externum ipsum humanum corpus certo quodam modo determinat. At quatenus externum corpus individuum est quod ad corpus humanum non refertur, ejus idea sive [mng eqv]  cognitio in Deo  est ... quatenus Deus affectus consideratur alterius rei idea quae ... ipso corpore externo prior est natura. Quare corporis externi adaequata cognitio in Deo non est quatenus ideam affectionis humani corporis habet ...
{2p28 ideae affectionum corporis ad mentem referuntur non clarae}   ...to make it worse, we do not fully understand the thing that receives the impacts: our own body...
...The ideas of the modifications [Lat: affectiones] of the human body, in so far as they have reference only to the human mind, are not clear and distinct, but confused. ... Ideae affectionum corporis humani quatenus ad humanam mentem tantum referuntur, non sunt clarae et distinctae sed confusae.
...The ideas of the modifications [Lat: affectiones] of the human body involve the nature both of the human body and of external bodies ... they must involve the nature not only of the human body but also of its parts; for the modifications [Lat: affectiones] are modes ... whereby the parts of the human body, and, consequently, the human body as a whole are affected. But ... the adequate knowledge of external bodies, as also of the parts composing the human body, is not in God, in so far as he is regarded as affected by the human mind, but in so far as he is regarded as affected by other ideas. These ideas of modifications [Lat: affectiones], in so far as they are referred to the human mind alone, are as consequences without premisses, in other words, confused ideas... ... Ideae enim affectionum corporis humani tam corporum externorum quam ipsius humani corporis naturam involvunt ... nec tantum corporis humani sed ejus etiam partium naturam involvere debent; affectiones namque modi sunt ... quibus partes corporis humani et consequenter totum corpus afficitur. At ... corporum externorum adaequata cognitio ut et partium corpus humanum componentium in Deo non est quatenus humana mente sed quatenus aliis ideis affectus consideratur. Sunt ergo hae affectionum ideae quatenus ad solam humanam mentem referuntur, veluti consequenti absque praemissis hoc est [mng eqv] ... ideae confusae ...
{2p35 Falsitas consistit privatione}                                            ... inadequate ideas are not false, but internally badly ordered and connected, incomplete, confused...there is no such thing as falsity ...
... Falsity consists in the privation of knowledge, which inadequate, fragmentary, or confused ideas involve. ... Falsitas consistit in cognitionis privatione quam ideae inadaequatae sive [mng eqv]  mutilatae et confusae involvunt ...
{2p36 ideae inadaequatae et confusae eadem necessitate} ... inadequacy is NOT a property of ideas in themselves but of the relations (ordo et connexio) of ideas in an imperfect mind ...
... All ideas are in God ... and in so far as they are referred to God are ... adequate; therefore there are no ideas confused or inadequate, except in respect to a particular mind ... ... Ideae omnes in Deo  sunt et quatenus ad  Deum referuntur, sunt ... adaequatae adeoque nullae inadaequatae nec confusae sunt nisi quatenus ad singularem alicujus mentem referuntur ...
 
{2p38 omnibus communia non concipi nisi adaequate}   ...a criterion of adequacy if: being common to all...
...Those things, which are common to all, and which are equally in a part and in the whole, cannot be conceived except adequately... ... Illa quae omnibus communia quaeque que in parte ac in toto sunt, non possunt concipi nisi adaequate ...
{2p38c dari quasdam ideas omnibus communes}               ...hope from {2p38} (the return  of the common denominator): all human bodies agree in certain respects hence adequate perception is possible!  ...
...there are certain ideas or notions common to all men; for ...all bodies agree in certain respects, which ...must be adequately or clearly and distinctly perceived by all.  ... dari quasdam ideas sive [mng eqv]   notiones omnibus hominibus communes. Nam ... omnia corpora in quibusdam conveniunt, quae ... ab omnibus debent adaequate sive [mng eqv]   clare et distincte percipi ...
{5p31 Tertium mente aeterna}                                                   ... formal cause means the same as adequate cause ...
...is the adequate or formal cause of such knowledge... .... causa est adaequata seu [mng-eqv] formalis...

Equivalence claims involving idea (cognitio) adaequata
{2d04} [notes] 1. adequate idea 2. an idea which, in so far as it is considered in itself, without relation to the object, has all the properties or intrinsic marks of a true idea. 1. [ideam] adaequatam 2. [ideam] quae quatenus in se sine relatione ad objectum consideratur, omnes verae ideae proprietates sive [mng eqv]  denominationes intrinsecas habet.
{2d04} [notes] 1. properties 2. intrinsic marks 1. proprietates 2. denominationes
{2p11c} [about perception] 1. partial 2. inadequate [De perceptioni] 1. partesive 2. inadaequate
{2p25} 1. an adequate knowledge of the external body is not in God, in so far as he has the idea of the modification [Lat: affectiones] of the human body 2. the idea of the modification [Lat: affectiones] of the human body does not involve an adequate knowledge of the external body. 1. corporis externi adaequata cognitio in Deo non est quatenus ideam affectionis humani corporis habet 2. idea affectionis corporis humani adaequatam corporis externi cognitionem non involvit.
{2p29} [About the ideas of affections of the human body] 1. do not involve an adequate knowledge of the said body 2. does not adequately express its nature 3. they do not adequately agree with the nature of the mind 4. the ideas of such ideas do not adequately express the nature of the human mind 5. [the ideas of such ideas] do not involve an adequate knowledge thereof. [De ideis affectionis corporis humani] 1. adaequatam ipsius corporis cognitionem non involvit 2. ejus naturam adaequate non exprimit 3. cum natura mentis non convenit adaequate 4. hujus ideae ideam adaequate humanae mentis naturam non exprimit 5. adaequatam ejus cognitionem non involvit.
{2p34} [About ideas in us] 1. absolute 2. adequate 3. perfect [De ideis in nobis] 1. absoluta 2. adaequata 3. perfecta
{2p35} [About ideas] 1. inadequate 2. mutilated and confused. [De ideis] 1. inadaequatae 2. mutilatae et confusae
{2p36} [About ideas] 1. adequate 2. clear and distinct  [De ideis] 1. adaequatae 2. clarae  ac distinctae
{2p38c} [About perception] 1. adequate 2. clear and distinct [De perceptioni] 1. adaequate 2. clare et distincte
{4p23} [About doing] 1.  he does something, which is perceived through his essence alone 2. which adequately follows from his virtue [De actioni] 1. ipsius essentiam percipitur 2. ipsius virtute adaequate sequitur
{4p27} 1. has adequate ideas 2. reasons [About the mind] [De menti] 1. ideas habet adaequatas 2. ratiocinatur
{5p28} [About ideas]  1. adequate 2. by the second and third kinds of knowledge [De ideis] 1. adaequatis 2. ex secundo et tertio cognitionis
{5p31} 1. adequate cause 2. formal cause 1. causa adaequata 2. [causa] formalis